Is my Islam acceptable, even though my conviction in it did not come about by discrediting Christians for saying that Jesus is the Son of God, but rather based on my conviction that Islam came with the details for everything, and that it is a religion that directs human life, and because of the miraculousness of the Holy Quran?

We give glad tidings to the questioner that Allah Almighty accepts those who embrace, believe in, and adopt the correct religion, regardless of the reason that led them to it. The important thing is the presence of the correct belief, and she must solidify this belief by learning about Islam from the Quran and the authentic Sunnah (definition), for the strength of faith and the soundness of belief increase with increasing knowledge. It is recommended to read the series "Al-Aqidah in the Light of the Quran and Sunnah" by Dr. Omar Al-Ashqar, and to ask scholars when encountering difficulties.