I would say, you can forgive her, and when you are in Christ you must do so. It doesn't happen over night, but then again, her choice to betray you didn't either.
Having said that, she's your girlfriend, not your wife.
You can forgive and let go. The choice is yours. The one question you may wish to ask yourself is,
do you trust her?
Take a while to find that answer given what the question entails. Do you trust her: Not to cheat again, not to lie to you, not to betray your trust again.
If the answer is no, move on. That's my advice. If you can't trust someone you can't truly like them. If you can't truly like them you can't love them. Like comes before love, and trust is woven into both.
God be with you.