Trying to hook up with another girl for the sake of getting over her isn't right for you, or for the other girl (been there, done that). I think the question you ask in your thread title is impossible if you love the girl, especially for a first real love like you've described. You can get over her, but it certainly will not be fast. I would love to come on here and give you a reassuring answer of "do THIS and your heart will be free and clear" but i'm gonna do you one better and give you a straight answer. It's not gonna be easy, it's not gonna be fast, it will be painful at times, but I believe that in the end you will be able to get over it and be better off than your were before.
Getting with another girl and getting better yourself are two independent things. Bottom line is that if this just happened, you aren't really ready to be with another girl just yet. If anything just make female friends right now and take it real slow. The most important thing is to get yourself right by any means necessary. Whether that be going to the gym, or having some other kind of outlet like writing music, going out with friends, etc etc... Keep doing these things so that you don't spend too much time dwelling on your own thoughts. If she's with another guy, I think that at least for now the no contact rule is your best friend. I know how it can be when the girl you love is with someone else and saying she will leave him for you. It happened for more than a year with me and I stuck around all that time as the backup guy until I finally smartened up and realized she wanted the comfort of both without having to really choose one. Actions speak louder than words, and if she wanted to break up with him and get back with you, she wouldn't have just talked about it, she would've done it. So your job is to not let her have you anymore. Good luck bro.
Be careful with your heart, because when someone seems too good to be true, they usually are.