Should I forgive her?

Really it depends on if she's changed or not. Looking at what you've written it seems she can't be trusted. The best thing for you to do is find a way to speak with her and let her know how you feel. Be calm and be the better person. If she says she's sorry tell her that you prefer actions over words and see if she stops backstabbing you, if not then I would let her know that she had her chance and she blew it. Good luck!