There is no such thing as a perfect girl, or guy. IF she was perfect think about it, are any of us, worthy of someone who is perfect?
We all have things we do and don't do that another person is going to hate at times. There has to be, so that there can be some low level of conflict within a relationship. We all have to have this to keep a relationship intersting and active.
And all relationships have to grow.
Now I am not sure exactly the ages you are talking about for her and you right now, you are 20 now? Not when you started. She is now 16 ?
If so that is in itself part of the issue, during the 14 to 18 year old stages people are still kids, growing and changing.
Add to that possible abuse issues and that is totally a problem situation.
Now you "love" her, but are you IN LOVE with her. A person who is truly in love will see what a real problem is, and will then work to solve the problem.
Is there still abuse at her home, if so something needs to be done, even if there is not current abuse, the previous abuse should be reported,
Next she needs counseling to come to grips with her emotional and sexual issues.
Love will go to all limits to make it work.