This is an incredibly large question, and makes more than a few assumptions that we need to look at.

To start, the Trinity is a way of understanding the nature of God, but is not a concept that is explicitly labeled or defined in the books that make up the Christian Bible (as defined by Catholic, Orthodox, or Protestant Churches). The three persons of the Trinity (the Father, Son, and Holy Ghost) all appear or are referenced in books of the New Testament, but the nature of the relationship between them is not fully attested to.

Trinitarian theology developed in Late Antiquity as a way of understanding that relationship. It was developed by Christian writers over the next five hundred years or so alongside a number of other theologies, but became the “mainstream” understanding of Christians in the Greco-Roman world for a number of reasons varying from the theological to the political. From that basis Trinitarianism would become the understanding of the churches that continue to ascribe to the ecumenical creeds formulated of that time period, including the Orthodox, Catholic and (much, much later) Protestant churches. However at no point have all Christians been Trinitarian, including in the current day.

The theological nature of Christ as a figure both fully God and fully human is likewise a subject that was much debated, and continues to be so. How much Christ is God and how much Christ is human is a subject about which much ink and blood has been spilt.

Just some of the Christian groups that differed from the Trinitarian norm include the Adoptionists, the Apollonians, the Arians, the Bogomils, the Docetists, the Pneumotomachians, the Monarchianists, the Monophysites, the Monothelitists, the Nestorians, the Patripassians, and the Sabellians. And that doesn’t even get into the Gnostics.

Islamic understanding of this is a whole separate question.

The understanding of history presented in the Qur’an is that the Prophet Muhammad is the last of a series of prophets who had preached God’s true message, but that over time each of those precious prophet’s messages had been corrupted. From a rhetorical perspective this has the interesting result of legitimizing Muhammad as part of a longer prophetic tradition while elevating him above precious prophets whose messages didn’t take. Declaring that Trinitarianism is such a corruption is an argument for selecting Muhammad’s teachings over those that came before, but there is some argument as to whether the Trinitarian position is accurately described in the Qur’an.

Your question as to whether or not the Bible was altered to be more Trinitarian is a third, completely separate question. The New Testament alone consists of 27 books written by at least a dozen different authors in different parts of the Greco-Roman world during a timespan of around a century which were passed around and copied between churches and for which we have no original manuscripts. Studying these works were selected and edited is a question that scholars turn into careers with great regularity.

To further complicate the question, when asking about whether the New Testament was manipulated as a canon/collection, there is a chicken-and-egg relationship with the theology, as it was the same Christians who were debating Trinitarianism over the next few hundred years who determined what was in the collection and what was out.

The question as to whether the Old Testament/Hebrew Bible aligns with the New Testament in understanding the nature of God, let alone attesting to a Trinity, is yet another complicated question.