I never ever thought I would cheat, but I did and I think I get it now. I agree with the anons saying don't tell, compartmentalise and forget about it. You should ultimately ask yourself if this relationship is for you, chances are it isn't and you should probably break up. Even if you do break up, don't tell her that you cheated, there's no point.
I was totally head over heels for my girlfriend, then she did something just to spite me and prove I 'don't own her', and then didn't talk to me for a few days. I thought we were going to break up, then she apologised and acknowledged that it was dumb. I accepted the apology, but maybe I shouldn't have because I just haven't seen her in the same way since. I cheated on her about a month later with a tourist. that was last year, I'm still with my girlfriend, and the other girl still sends me nudes lol. I still care about her, but when I cheated I realised that it's nowhere near as much as I did before. I know what she did doesn't justify me cheating, but I did what I did either way. We'll break up eventually, but I can't bring myself to do it out of the blue because she'd be devastated. I'm trying to slowly separate myself from her.
That was a bit of a tangent but my advice is don't tell, don't do it again (you fucked up by cheating with someone within your existing social circle, the girl I cheated with still thinks I'm single) and you should probably break it off.