I won't say i have the same problem but i had a very similar problem.
The first few weeks are uni are full of awkward small-talk, you meet heaps of people you'll never see again, it happens. I was terrified of meeting people and talking to new people (strangers) and yet, i wanted friends so badly. The first few months (and i guess year-ish) of uni, i basically had no close friend groups or anything i saw outside of labs.
I mention the above for two reasons:
(1) It does get better, groups and classes get smaller. You get better at it. If you're thrown into a situation where you have to do something, the human brain, mind and body is incredibly adaptable. Think of all the great feats people have accomplished under pressure, you may have even noticed it yourself as well. Think oral presentations or other stressful situations in the past. It did suck but you got on with it, you actually did it. So, you can do this, you can do it again. Meeting strangers gets easier, talking to people gets easier, it all does with time and just being thrown into it and forced to do it.
Indeed, some psychological therapies for social anxiety are actually just gradually introducing you (/throwing you into) situations that are somewhat uncomfortable for you. You gradually get use to it and better at it, these things are backed by research.
(2) Good news, you can make your situation better, you have that power, it's a really cool super power. The downside is it requires effort and it'll be scary and suck at first. It's like if you have a cut and go to the hospital, it hurts to get the stitches but its ultimately to help you for the best. You can improve your situation greatly by just trying to put yourself out there as much as you can (even something is better than giving up and doing nothing). You can also join various clubs, at large universities, there are so many clubs you are bound to find something you are interested in. This gives you one easy way to meet people (you all have to be in the same room) and something to talk about already (what the club is about). It might be scary to go at first but really try promise yourself you'll at least try it a few times.
Another way is to try propose study groups to people you have met (or even just ask on your universities facebook/stalkerspace) you might meet friends that way as well.
Lastly, another great perk of university is free counselling, if you think you could even benefit from it a tiny bit, i'd take the appointment. If you dont like it, you never have to go back again, they wont force you. It very may well help you though. There doesn't need to be anything "wrong" with you to need to go either, we're all imperfect, counselling can help anyone improve on things they want to improve.
Too long? : Hang in there, it gets better. You have the super power to make your own situation a lot better with some small steps. At the very least, stick out uni for a few more weeks before you decide you can't go there at all. Look up the census date, you can drop out before this date without any financial penalties. Afterwards, you will owe a HECs debt for the units you have taken, there are procedures to get it cancelled though (for a good reason).