I'm sorry, I have to agree with sfalexi. I mean, c'mon... this wasn't really an accident if you purposely tried to meet up with this girl.... and you invited her over for a movie alone in your room? Hm. Really now.
Plus, if you really solely and truly were committed to your girlfriend the problem with telling the "other girl" wouldn't even concern you. She is a female you cheated on your girlfriend with, what would you care if she hated you so long as you and your girlfriend were okay?
Whether its consciously or not you have other ideas that don't involve being completely faithful to your girlfriend. I think it's best for her if you at least take a break from your relationship to figure yourself out. I apologize for being so harsh, but this is the way I see it.

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I have seen the mystics play there,
Once or twice but I knew they had a reason.
Enchantment plays it's cards all right,
Hand in hand with the working of the seasons.