Are we talking about sexual cheating here, as in she slept with someone else? Or did she kiss someone else or go out with someone else?
What was your agreement? Had you agreed not to do whatever it was she did with anyone else? Or was that your assumption?
At your age, your brain is filled with a lot of emotions and, unfortunately, not a lot of wisdom or experience. Don’t worry, you will get the other two. But the hardest thing to do is to hold off all your most vile emotions. The need for revenge is a vile emotion. It is a fairly useless emotion. It does not help you.
Your girlfriend is probably pretty immature. Who knows why she did what she did? It might help you to find out, if you want to talk to her about it. I always wanted to talk to my girlfriends after they did things that hurt me. It helped me understand to hear from them. Of course, at 14, she may not have a clue why she did what she did, so that may not help.
But I would try to talk to her and to see what happened. Then I’d agree on where to go next. I would resist as much as possible listening to what anyone else said I should do or feel. I would make my own choices based on what she says, not what other people say.
Those people who showed you the emails? They aren’t your friends. They are trouble makers. If I were you, I would break up with them, too, assuming you still need to break up with your girlfriend after you talk to her. But do not let social pressure determine what you should do. Other people just want trouble. They want to see drama. You need to find out from your gf what actually happened. If she’ll tell you. If she will tell you the truth. These things may be hard to know.
But use it as an opportunity to learn to express your feelings. Don’t blame her. Talk to her. Tell her your story. Tell her how it makes you feel. Own your own feelings. She isn’t making you feel anything. You may not like her behavior—that’s fine. But don’t blame her for however you feel. You are responsible for your own feelings.
I’m really sorry you have to come to a place like this to get advice on this problem. We don’t know you or the situation, and because of that, we will give bad advice. You must keep your own council and work things through. But revenge? Should not be a part of it. You don’t know why she did what she did, or even if she did what she did if you haven’t had a long, honest talk with her.