I think the OP is right when he states this relationship is a "crush." It is infatuation, and has nothing to do with the Biblical concept of love, especially in marriage.
First, you cannot fix anyone but yourself. If she is emotionally disturbed, has a temper, etc, all the "love" in the world isn't going to change her. In fact, without Christ she is likely to get worse and worse.
You cannot love this woman, because you do know really know or understand her. If she converts, she will lose her family and friends. Not that it would be a terrible thing, but you know the consequences of that already.
If you convert to Islam for her, there is no firm commitment that she will marry you, or that the marriage will work out. Then there is the most important fact - if you walk away from Christ, you are going to hell. If you ever were truly saved in the first place.
My conclusion is spend the next three weeks studying for your test. Put her out of your mind. When the exam is done, see if she understands who Jesus really is, and if she wants to give her life to Christ. If not, you have your answer. Move on, and leave this person behind, forever.