It's really a matter of how much you 2 care about each other and how willing you are to try to make it work. And anyone who says that 3 months is not enough time to love someone is full of crap...there is no TIME LIMIT on when you fall in love with someone..it can happen in an instant or a year or longer.
I've dealt with this quite a bit being in the military and moving around so much and even though I'm mostly an utter failure at relationships I can say a few helpful words on this subject.
Know that it will be VERY HARD to make it work. You both have to have a very strong trust in each other; otherwise insecure thoughts are going to creep into your minds and accusations of cheating and things of that nature will begin to fly. Do you see yourself having a future with this girl? Like possible marriage one day and all that? If so then I'd say definitely try to work it out. If not, then you have to decide if you want to continue through the unavoidable diffuclt times ahead with a long distance relationship just to see if your feelings change and you do decide you want more...whether or not it's worth it only you know.
As far as the college thing: yeah I'm sure you will have tons of fun and plenty of opportunity to have wild sexcapades and all that. You have to ask yourself: Is screwing a bunch of college girls worth giving up what you have with your current girl? Again, you're the only one who knows the answer to that. If you are unsure to the answer then I would say either go the "see other people" route or break it off. Otherwise the relationship will probably fail because it was never that strong to begin with and you will end up resenting her for in your mind "denying me the chance of a lifetime to live it up at college"
Good luck with whatever you do decide and good luck in college as well.