my girlfriend says she cant get over my cheating

me and my girlfriend ahve both been dicks when we were drunk. we were seeing each other for like 4 weeks. then when i was so drunk my freind came onto me and we ended up kissing. me and my girlfriend broke up cause of it. but then got back together later on. but every so often she would break up with me then go with another guy saying she just could not get over what i did. i took it for a while until i got ridiculous. then she begged for me back. saying she promised she would change and would get over it. but now a few weeks later she is saying is not so sure any more. what do i do? i have to break up with her cause she is saying she would just cheat on me agian. but i love her so much. she says if i spoke to that girl in town, hu is my frined, she would just go and cheat one me. is there anythin i can do. i lover her so much!

please help