She cheated on me, now she broke up with him and wants me back?

So few months back I had a hot af and popular girlfriend, that I caught cheating on me (kinda). She thought I wanted to break up so she did it herself: There was this guy having a crush on her for a while, and once she thought that I wanna break up she got together w him. I found out she was cheating on me so I obv got mad at her. The reason she told me that made her cheat on me was thinking that I wanted to break up myself.
We have not talked for a long while untill I found out thw broke up. We started talking and she told me that she loves me, and that she regrets doing all the shit she did. Now we kind of got together again but we just had a fight, a guy told her that she's his crush, and she posted that on facebook although we were together. I got mad again, she explained this (she met him at a dance club thingy and he didn't let her go, and that she does not like him). I am not sure what to do, trust her although she cheated on me once or break up? Please be descriptive in your answers and tell me exactly what to do. If you need any more info bout something just ask me. BIG NOTICE:We are having a distance relationship, there are like 5-6 h to get to each other.
Again, be really descriptive and tell me what to do, I really need help.
Break up (please, give a longer opinion)
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Keep it going (give a longer opinion)
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She cheated on me, now she broke up with him and wants me back?
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