Hi, I'd like to help you with your question.
Yes, couples can recover from infidelity. It takes work, in particular a rebuilding of trust, but it is very possible.
The first thing that needs to happen is your girlfriend needs to own up to her behavior.
Has she admitted to what she did and told you that she is sorry?
Has she explained why she cheated?
Has she broken off any and all contact with this person?
These things must occur before trust can be rebuilt.
Another important step is allowing you to ask any questions you need to about the affair. This may make your girlfriend uncomfortable. But since she brought another person into your relationship, you have a right to know what you want to know so you can form a bond with her again. Anyone who hides or refuses to share what happens in an affair keeps that affair between themselves and the other person. This is like a secret your partner has from you and won't share it. It also continues the bond between your girlfriend and her lover and breaks trust and the bond between you. Plus it leaves the affair/relationship open to your interpretation and imagination. And that is worse than reality. It will keep coming between you and your girlfriend until it is no longer a secret.
The next step is therapy. Both of you need someone who is neutral to help you break down your feelings about what happened and re bond with each other. A therapist can help you both realize your feelings about the affair, deal with them and learn to trust again. To find a therapist, talk to your doctor for a referral. Or, if you attend church, your pastor could help. You can also search on line at http://therapists.psychologytoday.com/rms/.
There are also other resources to help you work on this at home:
Infidelity: A Survival Guide by Don-David Lusterman
Not "Just Friends": Rebuilding Trust and Recovering Your Sanity After Infidelity by Shirley P. Glass and Jean Coppock Staeheli
Surviving Infidelity: Making Decisions, Recovering from the Pain, 3rd Edition by Rona B. Subotnik and Gloria Harris
You can find these on Amazon.com or your local library may have them for you.
I hope this has helped you,