I'm putting together a backstory for a D&D character who comes from a region analogous to China (Tian-Shu from Pathfinder in case anyone is wondering). My current backstory is that she's the illegitimate daughter of an upper class family and I'm just looking for a bit of real world history to flesh that out.
It depends on situation to situation. However, since your character is a female, she would be suffering a fair bit.
It ancient China, bloodlines are very important, and it links directly to the status of a person (as well as the inheritance that may come with it).
A son born to the legal wife of a man would be considered the proper heir 嫡子, and would have first consideration in inheriting all estates and titles when the man passes away. This status would be irregardless if the age of any of the other sons the man may have with other women. As such, the proper heir would be pampered the most in the family, and given all the best benefits possible. Only when the proper heir has brothers by the same parents, would there be a question of inheritance.
A son born to a concubine of a man 庶子 would be considered part of the family, but would not stand to inherit anything. If his mother was especially pampered, he may be allowed certain privileges, but these would still be considerably less than that provided to the proper heir. However, if the man has no son with his legal wife, the concubine's son may be promoted to be the heir, often through having the legal wife adopt the son as her own.
A son who was illegitimate, however, would not be treated as part of the family at all. Although the term 庶子 was also used to describe such sons, if their mother was not married to their father, they would be regarded as outcasts, and most would not be even allowed to enter the family home. Even if the birth father did show some concern for the child by bringing him into the family, the boy would often be mistreated. As such, they would have no chance of inheriting anything from the family. The only exception would be if none of the man's wives or concubines have sons, in which case the illegitimate son would be adopted, but would have to cut off all ties to his birth mother.
The most famous examples would probably be the uncle-nephew pair Wei Qing 卫青 and Huo Qubing 霍去病. Wei Qing was the illegitimate child of Wei Ao 卫媪 and Zheng Ji 郑季. Wei Ao was married to another man, and life was difficult enough for the family's existing children (Wei Ao already had one son and three daughters with her husband), so she sent Wei Qing to live with his father instead. However, Wei Qing's father made the young boy shepherd sheep, and the legitimate children in the Zheng family bullied him, ordering him around like a slave. Thus he decided to go back to his mother's family, and was employed as a stable boy by his mother's mistress (princess Pingyang 平阳公主).
Huo Qubing was the son of Wei Qing's sister Wei Shao-er 卫少儿 and Huo Zhongru 霍仲孺. Huo Zhongru was fearful of acknowledging his son (most probably because Wei Shao-er was a serving lady to princess Pingyang, and he might be punished for being with her), and so Huo Qubing had to grow up being part of the servants in the princess' house. More fortunately for him, his auntie Wei Zifu 卫子夫 soon won the emperor's favour, and he was brought to court to be brought up and became a general at the age of 19.
These information would only apply to sons, because sons were the ones who stood to inherit family estates. Taking your backstory into consideration, a daughter born to an upper class family would be reasonably well brought up as a lady, and would be married off at a suitable age to be a bride to a (hopefully) rich or powerful family. However, an illegitimate daughter would not be accepted into the family at all, and would have to live off whatever her mother's family could provide for her.
If her mother's family had enough money, she may still have a relatively easy life, but would not be permitted much freedom as it would be considered a family shame to let her be seen on the streets. She would also be married off as soon as possible to cut off her ties to the family.
If her mother's family did not have money to provide for her, she would probably be sold off - if fortunate, to a family that has no children and are looking to adopt; if unfortunate, to the brothel so that her mother could gain some quick cash. The family would not want to keep her, since an additional person means an additional mouth to fill.
Hopefully, these information helps out.