OK I have recently been with her for about a month but her last boyfriend was her first real relationship and I think she still has feelings for him even though it turned out to be a bad relationship like he cheated on her and stuff and she ended up breaking up with him and he still isn't over her and her him I think but she is trying to move on and I just don't want to loose her.

Well if she has unsettled feelings there is really only 2 options for yourself. If you feel her sliping back to him you can.
1.) Sit there do nothing about it be jealous and insecure and eventually lose her because of it.
2) Show her how you can really treat her, make her realize why she is with YOU and not him.

Also sometimes it just takes time to get over your first real relationship. I just broke up with my GF of a year about a month ago it was my first true relationship and I'm still not even close to getting over her. Even though I say I already am. So stick with it, try not to get jealous and try to let her know that your serious about her and can offer her so much more than he can. But some times Expo1 it's better to just let people go if they are not over their ex's at least you know only 1 month into it.

How long did she break up with her boyfriend before your starting dating?