So my bf and i have been dating for almost 5 months

when we first got together we had some drama with his ex , she would email me saying they have been seeing each other and so on. She forwarded me texts that were from his number and so on.He denied and denied.

Every so often she will still message me saying these things but shes always been the liar and a back stabber people say
I seem to always check his facebook and read his stuff to see if he's been talking to other girls. i read one of his im's with his friends and them talking about going out of town to pick up girls, who knows if is will ever happen.
I also saw another message him giving his number to a girl. i confronted him about it and she was just a friend from school.
The other day he left his phone account in my laptop i checked his calls and there was some from his ex who messages me. the calls were recent.
I feel bad for being sneaky, but i feel like i have the right to be. and i need to be.
There has also been a lot of negative feedback from people about him.

He's had a past and fessed up about it, but im not sure if he was just saying that.

AT other times he is the nicest guy in the world and takes care of me and loves me.

Im honestly just confused, i sometimes just feel like ending it, but at other times i feel like i need to work it out/

advice please!