Should I stay with my girlfriend?

I started dating this girl who I have been friends with for about eight years. We started hooking up a year ago and have been officially dating for nine months. This girl is beautiful, funny, fun to hang out with, we have great sex and she is one of my best friends. When we are having a good time it is awesome and I can safely say I have never loved anyone as I love her, but she has shown from the very beginning of us dating and still to this day that she is a liar and probably isn’t over her ex. I want to know if I am being paranoid and jumping to conclusions or if I am just convincing myself that everything is ok.

The first time I found out about her being shady was on valentines day, she had sent her ex texts saying that she was still always thinking about him and still loved him, so we broke up after her ex sent me the texts she sent him. Later that day I ended up back at her house and we made up. The next month she lies to me and I find out she is going to jail to visit her ex. We break up get back together right away. A few months pass and I’m looking for some clothes for my son and find some love letters that he has been sending her. She says she never wrote him and kept them because she thought he finally cared about her but that she wanted to be with me and that she would write him a letter saying that. She does.
One of the dudes friends hits me up saying he is angry at me because my girlfriend ( his ex) told him I made her write that letter. ( which is a lie) we break up for about a week she tells him that was wrong of her to put that blame on me and that she just didn’t want him mad at her. We are currently living together and I feel stuck. I have no idea what to do. I don’t know if I’m being crazy and it’s not a big deal and she really does love me, or if I’m just buying into what she says and can’t except that she’s not over her ex. Any advice or personal experiences?