I cheated and I feel really bad.

Well I've been with my girlfriend for three weeks, I know its not a long time but I like her. She went away for a night with her family and I went into town with my friend last night to go to a bar. I saw some people I knew so I went over and met the other people they were with. I met the girls they were with and they were celebrating one of the girl birthdays. We were going to leave but the birthday girl told us to stay, so we did. I got talking to her and we got along nicely. Later I was speaking to some everyone there, drinking and I was pretty drunk by 11:30. The birthday girl came and sat next to me leaning on me and we talked for the next half an hour. At 12:00 it was her birthday. So when it was her birthday we all sang happy birthday and then when we finished she kissed me, then we started kissing for a short time. Later that night we kissed again and then she left. I know she doesn't want a relationship, just a bit of fun. Now I feel really bad and regret it. My girlfriend wants to go out tonight. She was cheated on by her last boyfriend and is really sensitive about this. A few days ago she texted me saying "If you ever cheat on me please, pretty please don't be a douche bag and not tell me, don't even think about not telling me ok? Honesty is really important in a relationship". I know she will find if I don't tell her but I don't want to break up with her :( How would you feel girls and would you break it off if a guy did the same to you? Any experiences guys? How can I tell her?
I cheated and I feel really bad.
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