if you can afford it, therapy is always not a bad idea to at least try.
but what you're feeling, like your youth has been cut short, i can guarantee you almost everyone on the planet feels to some degree. also: teenage/college parties are a lot more hellish than you are probably romanticizing them to be. a lot of kids getting way too drunk and high, some overdosing mixing booze with pills, a lot of unwanted sex with intoxicated people, it's really kind of awful.if I were you, I would focus my therapy more on encouraging socialization, they will help you figure out ways to ease up to it and fight cognitive distortions you have regarding meeting new people.
if you focus your therapy on this feeling of 'missing you' you are likely to never get anywhere fruitful - that feeling of a 'missing' piece of ourselves somewhere out in the world is pretty much just the instinct that gets us to meet people and not die alone. there are a lot of opportunities now more than ever to meet people through the internet, find small niches you enjoy and talk to other people interested in them. i'm not really one for bars or 'normal' spots to socialize i can really relate to feeling cut off in that regard. but there are millions of people out there just as eager to socialize as you are, and probably a lot of them coming from a similar place of struggle with anxiety.