Should I break up with my girlfriend or not?

Me and my girlfriend have been dating for about 1 and 4 months now , not counting when we broke up before school ended and then got back together in the next school year anyways me and her have had a lot of issues lately and I've been dealing with it for months now and I don't know if I should just end things with her. I'll start by saying what's going wrong and then I'll say what is good about it. First off my girlfriend has had history with some guys at school and she acts very friendly with them and is touching them stuff like that and it makes me made because she would tell me not to do stuff like that with people I have had history with. 2nd she likes to lie about things and thinks she can get away with it she has also in the past went behind my back to some dudes party to keep in mind. 3rd she gets mad over the little things easy and she worries about the negative things way to much and it seems like we spend more time arguing about something then loving each other. The good parts are first off she really really really loves me and she is also my first love keep in mind I haven't been in a relationship this long before anyways we have already met each others parents and went to prom together once and we have done a lot of fun things together she also doesn't give up on me she is relentless lol anyways yeah I want to know what I should do? Thanks
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Should I break up with my girlfriend or not?
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