She has an emotional baggage and is wielding it as a self defense weapon. She has low sense of self worth to the point that she doesn't believe anyone would like her at all, and I'll bet it's because she doesn't like herself.

Considering her past, it sounds like you'll be walking on egg shells around her because whatever you do, she'll imagine that you have something going on behind her back. Since you're already in the relationship, I suggest putting in the effort to help her fix herself. But first, she needs to be open to that idea so you'll have to talk.... You can do your part to be faithful and loving, but can she do her part of loving herself and not attack anyone who tries to be nice to her?

It can also mean 6 years of bitterness and grudges against her cheating ex, so it's not really a good justification. There are a few things I learned being in a relationship:
- not all truths should be said. There is a time and place for truth, and sometimes you bring one to your grave.
- commitment to one is not just the loyalty, but also the strive for good times together. If you know your actions will hurt your partner, then don't do it. Why be together if you only want to spite him/her?

There's a reason why she's saying those things, my guess: she is seeking some sort of negative validation like, "everyone cheats" and it's not healthy for the both of you. As it is now, she doesn't even acknowledge her own issue, so good luck trying to fix it....