The most important point is also the worst - try not to worry about it. If you're anything like me, overthinking things related to social life is the single worst thing you can do.
If you're not naturally outgoing, make a point of finding things to do where other humans also do things. It is college - there's some interest group that you'll like. You mention a lack of time, but try to make some, even if you're tired.
Unless you have some specific goal[1], don't worry about what "type" of person you're hanging out with other than the type you get along with. Avoid hanging out with people you're not in to, just because they're there - find people you want to be around.
And remember, this is college - land of new adults, raging hormones, bad idea theater and awkward conversations. Most of the people around you are at least as neurotic about social stuff as you feel, and the ones that aren't likely suck to be around[2].
Finally, don't listen to me. College was a long time ago, I have three close friends (all of whom I've known at least 20 years), and I've lived in the same place long enough that I usually know a few names when I go somewhere, and that's more than enough for me. So I'm not exactly a social animal.
[1] I'd argue that having specific goals in social settings tends to make you think of other people instrumentally, rather than as having their own value outside of what they can do for you, and that leads to ugliness. But YMMV.
[2] There are genuinely well-adjusted, nice people out there, but they're fairly rare in the early 20s. The others are insecure jerks masking with overconfidence, bullies or sociopaths.
