Kindhearted anon with relevant experience here, ready to use my anecdotes to quell fear and bridge understanding!
This is pretty relevant to my current relationship. The whole very social + less social thing is true in my relationship except I'm the social one! As a highly extroverted person in a relationship with an introvert, let me say this: I love her so much and she makes me incredibly happy. Different levels of sociality (not a word but I'm using it anyway) doesn't have to be a roadblock as long as you can both be emotionally healthy enough to understand what it means for you two. As long as you don't mind her hanging out with her friends when you don't feel up to it and she doesn't mind you not coming along, there doesn't have to be an issue. Integrate if you like, but if you feel forced then it's time to talk to your partner about your feelings on the matter (you do talk about your feelings, don't you, anon?).
With that said, let me move to another point: growth mindset, baby! Like >>9781 said but in a way that doesn't tell you to give up on this girl, you can be in a relationship with her and become more social if that's something that you want. Getting a gf isn't the top of the mountain, you mustn't rest on these laurels. For your mutual happiness longterm (together or otherwise), you have to both still be growing. College is a big growth period, so definitely don't limit yourself in that regard (honestly you should keep growing after college, too, but that's another rant). Get the girl, keep developing, develop together and either
A) Grow stronger! As you continue your emotional development, you two may become an even more powerful power couple, complementing each other in ways few thought possible. DO NOT tether your growth to hers (and vice versa), though, as that is extremely unhealthy and after an inevitable break-up, you'll suddenly realize how much you were holding yourself down (this is experience talking again, so don't make my mistakes).
B) Grow apart. If this happens, it wasn't meant to be forever and that's fine. Hopefully you both got something out of it, whether that's good times, a better appreciation of what you want, or anything else. Don't fear the growing apart. It may be hard, but it's much better than forcing yourself to grow the same way.
It's not often that I get to give relationship advice because 1) nobody ever asks me, 2) few of my friends need it in the first place, and 3) fewer still know they need it. People only seem to ask for advice/input while courting and my friends don't court much. The point of this bit is just to say "Sorry if I've written a big ol' blogpost, but I feel like I know some things that I never get to tell anyone".
Now, as the Japanese say, Gunbutter!