Based on your first paragraph, this woman seems as though she is simply unsure of what she really wants. If she loves you and wants only you, then why is it she is easily infatuated with someone else ON A REGULAR BASIS as you seem to indicate?
That, coupled with her recently having sex with someone else, should be sending loud warning sirens through your brain. Even if the sex was not consensual, she put herself in a position that someone in a committed relationship should not have placed themselves.
All that said, whether you decide to forgive her and try to repair the relationship is up to you. You must decide if you can get past her cheating on you. But be aware that you may have to continue dealing with her indecision about breaking things off and then changing her mind. I sure wouldn't want to deal with that, but if you do, then great.
As an aside, IF things end between you, you will not be able to demand your money back from her for the tuition you paid on her behalf. Unless of course you have something in writing stating that you were loaning her the money. Otherwise, based on a 4 year relationship, it will likely be considered that you were simply paying for something for her because you considered the two of you a couple. But it would not hurt to ask her for the money back. lol
Good luck, whatever you decide.