A few quick points:
- Everyone makes mistakes.
- Do you really want your friends to control your love life?
- Doing hurtful things does not make you a hurtful person.
- Forgiving and Forgetting Are Two Different Things.
Ultimately, only you can determine whether or not you have the personal emotional strength to move forward with the relationship… If you're both willing and desire to do so, then the main issue you'll need to work on is how to rebuild trust between you, and how best to negotiate the boundaries of your relationship moving forward. Most of the time, cheating isn't about the sex, but rather about the betrayal/deception/lack of fidelity inherent in the act.
Depending on how bothered you are by the one night stand itself, you may even look into alternatives to the monogamous relationship style. Sometimes, the love you have can grow and thrive, regardless of what other loves may exist.
Assuming you'd like to continue the relationship, and that you would like it to remain monogamous, then the best thing to do is to stop leaning on your friends for support, and open yourself directly to your girlfriend – try to discuss how you feel about what she did, rather than about what she did wrong. Right or wrong, if it hurts you, that's all that matters in the context of your relationship. If she listens, and indicates a sincere desire to move forward, then set more explicit boundaries and limits – perhaps certain parties or outings tend to provoke her drinking to excess, for example, and should be avoided, or attended with you or not at all.
Finally, you finish your question by saying "I just love her too much to let go. :("… To me, the direct opposite should be true – if you truly love her, and respect yourself, you need to be willing to let her go.
Otherwise, it's entirely possible that at some level, you're more in love with having a girlfriend, then in love with your specific girlfriend. And that, my friend, does not bode well for long term happiness, and could even foreshadow a damaging cycle of emotional or even physical violence between you.