So as with all such questions, there are kernels of truth to what you may have heard. The difficulty lies in determining the extent of the truth, particularly when pre-Islamic or non-Islamic sources are scarce.

You touched on several themes in your question, which I will try to address below. I’ll start with a general discussion on how Islam affected the role of women before moving into two examples—the practices of veiling and female infanticide.

Women in Al-Jahiliyyah, or Pre-Islamic Araiba

I want to start with rebutting the argument that women in Pre-Islamic Arabia were entirely subjugated to men. In the jahiliyya, and within early Islam, women contributed to a number of facets of life. Women were soothsayers and prophetesses such as Sajah, a Christian woman of the Banū Tamīm who led a force of over 4,000 along with Musaylimah, “The Liar”, in rebellion against the nascent Muslim state. Like the previous sentence indicates, they were also involved in warfare. They were not only poets, telling stories of the battles and engaging in ritualistic pre-battle exchanges of insults, but also warriors themselves. Umm ‘Umara fought at a number of battles alongside men, eventually losing her hand at the Battle of ‘Uqraba in 634.

Sexual relations in Arabia were also more open than in those other societies, with both polygamy and polyandry being present. It was also common for them to remarry, showing there to be a lack of stigma against non-virgins, and often they brought significant wealth to these relationships. Muhammad’s first wife, Khadija, was one such widow. 15 years his senior, she was rich enough to allow Muhammad to not have to work, allowing him to instead focus on his spiritual teachings.

I want to be careful not to represent that women in al-jahiliyya lived absent misogyny or other societal restraints, as will be discussed below on Wa’da, but likewise want to make sure the diversity of pre-Islamic women’s activities is known.

Women in Early Islam

There was an undeniable shift in culture brought about by the rise of Islam. In some ways, Islam used pre-existing cultural traditions to help itself grow, or to make itself more understandable or palatable to the general population. One such example is the infamous “Satanic Verses” of Sura 53. In the early version, Muhammad permitted Muslims to worship three “daughters of Allah” alongside him, Allat, Manat, and al-‘Uzza. These verses were later abrograted, with Muhammad claiming that they were the result of Satanic suggestion that Muhammad mistook for revelation. The verses which replaced these Satanic Verses instead “point out the absurdity”, as Leila Ahmed puts it, of the idea that Allah would have daughters while mortal men preferred sons. In this way, Muhammad can be seen playing off both pre-existing religious sentiment and cultural sentiments regarding female children.

Have you ever considered about the (idols of) Lāt and ‘Uzzā, and about the other, the third (idol), namely, Manāt,? Is it that you have males and He (Allah) has females?

In other ways, Islam was purposefully constructed so as to be counter to the existing social structure. Muhammad instituted new laws regarding inheritance, providing a guaranteed inheritance to daughters and forbidding the practice of leaving widows as inheritance. The mandate to leave an inheritance to daughters is particularly important as there was already a custom in Mecca that allowed daughters to inherit, but from what I have read it had no legal weight behind it.

The various changes led to assertive and strong-willed women. ‘Umar ibn al-Khattab, who would later become the second of the Rashidun caliphs, allegedly complained about that “we the people of Quraysh [Mecca] used to have the upper hand over our wives, but when we came among the Ansar [Helpers], we found that their women had the upper hand over their men, so our women also started learning the ways of the Ansari women.”

Also in play was the religious framework that marriage operated within. Islamic law works through a local judge, a Qadi, issuing a ruling on a specific case so that it is in line with religious teachings (we have to note that there was no separation between the illegal and the immoral, but rather they were the one and the same). However, while the Qur’an protected women’s rights in a number of areas, judges often interpreted these not as legally binding rules, but rather as binding only upon the individual’s conscience. So, a man would not be legally bound to treat his 4 wives fairly, even if that is a stipulation within the Qur’an itself. There was, in essence, the loss of many Qur’anic provisions that could protect women.

Example 1 – The Practice of Veiling, an adaptation of an existing tradition

Veiling was common practice in multiple pre-Islamic societies across the Middle East, particularly as they urbanized. In Assyrian culture wearing a veil separated between a 'respectable' woman and those who were 'up for grabs', so to say. Upper class women, concubines accompanying those women, and former "sacred prostitutes" all had to wear it whereas normal prostitutes and slaves were forbidden from veiling themselves under threat of flogging or having their ears cut off. Ahmed then writes that this practice spread throughout the upper-class Mediterranean world—from the Levant through to Persia—and also crossed religious lines appearing in Byzantine Christian societies. Here, Ahmed gives the example of a 10th century Byzantine patriarch who wrote that he only allowed his daughter to go out "veiled and suitable chaperoned". She also notes the reasoning, separating the respectable from the rabble, remains constant even in these other societies.

However, that is not to say that veiling was necessarily widespread in Arabia itself. Women of the jahilyya pre-Islamic period did not normally don a veil. This of course varied from city to countryside, with cities being more likely to veil. Overall, nowhere was the veil common to the extent of places like neighboring Syria and Palestine.

Through Muhammad's entire life, the only women who were regularly veiled or secluded were his wives. Through successful revelations received by Muhammad, the practice of veiling and seclusion took hold among them, getting to the point where the phrasing "she took the veil" became synonymous to "she became a wife of Muhammad". Various impetuses pushed Muhammad towards these rulings. For example, Sura 33 was revealed after he became annoyed with guests staying too long chatting with his wives after dinner. Within Sura 33, verse 54 details that one should only speak to Muhammad's wives from behind a curtain. The word he uses for curtain is ḥijāb. Most westerners associate the word hijab with some sort of head-wrap of veil, but it also literally can mean 'veil' in the sense of a curtain. Verse 59 then gives the commandment to women to "bring down over themselves [part] of their outer garments. That is more suitable that they will be known and not be abused." This is allegedly in response to the "hypocrites", mere nominal converts to Islam, harassing Muslim women and claiming to have thought they were slaves.

Example 2 - The Practice of Wa'ada, the rejection of an existing tradition

Wa'ada is the pre-Islamic practice of infanticide through burying the infant child. Much of the impetus for this killing was economic, with it being seen even as a form of “mercy” for the child in particularly troubled times. However, the cultural preference for boys over girls also played an undeniable role. Males were seen as stronger and more useful for the family. Likewise, the possibility that a female child could be captured by an opposing tribe would bring shame upon the family.

Thus, while it was not solely female infants who were killed, the general conclusion is that the majority of the victims of this practice were girls (hence the phrase qatl al-awlād, which literally translates to "the killing of children", is often used interchangeably with qatl al-banāt, or "the killing of girls").
Al-Zamakhshari mentions two types of wa’d. The first is likely the one that you heard about. In it, a grave would be prepared in advance of a child’s birth. Any female infant was buried alive immediately after it is born, whereas males were permitted to live. This Pre-Islamic tradition is attested to in Sura 16, Verses 58 – 61:

“When one of them is told of the birth of a female child, his face is overcast with gloom and he is deeply agitated. He seeks to hide himself from the people because of the ominous [bad] news he has had. Shall he preserve it despite the disgrace involved or bury it in the ground?” (Sura 16:58—61).1

However, the second type of wa’d that Al-Zamakhshari recognized is not related to gender preferences but rather is a form of human sacrifice. Here, the killing of the child did not occur at birth, instead happening when the child was roughly aged 6 or older. This second type of wa’d is also alluded to in the Qur’an in [Sura 6, Verse 137)( https://quran.com/6/137?translations=17,19,21,84,85,18,20,22,101):

Similarly, their associate-gods have made the killing of their children seem fair to many mushriks (idolators), so that they may ruin them and may confuse their faith for them. Had Allah so willed, they would not have done that. So, leave them alone with what they fabricate.

While Qur’an officially and unequivocally condemns wa’d, it was not entirely wiped out by the rise of Islam. It was continually referenced throughout the medieval Islamic world, often as part of a sort of trifecta of birth control—coitus interruptus, abortion, and infanticide. It thus continued to be practiced but, due to the religious prohibition, it was assuredly less common and acceptable than in jahiliyyah.