Can't trust my girlfriend

Well im 20 years old and me and my girlfriend have been together 3 months and shes liec about a few things the first was that there was a guy she went on a date with couple of months before we met and I asked if they still spoke she said no but then I found messages from him that she had said she had a dream about him and he replied somethimg sexual but she told him it wasnt like that then he asked her to cheat on me with him and she told him she doesnt cheat but in my eyes thats somethimg you tell your boyfriend especially when she said she doesnt talk to him and the other thing is that I asked her if she kissed anyone while we went on dates she said no I later found out that she was at a party alone with a guy kissing him all night I know this was before we had a relationship but she still lied. I know to some people this seems stupid because its not a big deal but I have really bad trust issues as my dad walked out on me and my mum when I was 3 days old and shes the first person I e trusted to tell that and telo her I love her I dont know what to do ?