I always found that, after cheating, a person becomes very jealous / suspicious that the other person will cheat.
This is stupid, but, it is how people think.
Maybe she is worried you are going to go for a revenge fuck, or that, the reason you forgave her is because you ran around too.
Anyway,
I don't think you should move in with her, I think, you have to restart the clock after the cheating thing. That is, you have only been dating her for 2 months. Moving in with someone after 2 months is crazy.
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