OK so just to make this clear, the best thing is obviously if you can just relax and get out of that mindset, like lysergic_as_fuck advices. But you're struggling with social anxiety; that's the whole problem. You can't just stop caring about these things, it takes training. I used to have somewhat of the same issues as you (pretty much had to actively learn to look people in the eye when I was speaking to them at one point), and for me it took 1.5 years at an IT callcenter to fix it, talking on the phone for 7.5 hours 5 days a week. Basically just a ton of training in social interaction. Now I don't have any issues at all. I have a wife, 2 kids, and I honestly believe the insecurities I had earlier has made me more empathic than your typical extrovert. I can relate to insecurity and build people up when they need it now.
You just gotta go talk to a lot of people a lot of times, so try to look for workarounds for whatever issues you have until you are more comfortable. For low alcohol tolerance, this could be a possible solution?:
Read up on some facts about high quality alcohol, buy more expensive beers/whiskeys/cognacs, and try to come off as someone who prefers using their limited student money on high quality drinks. This is a totally valid thing to do. You can joke around about how you can't afford to get drunk on the drinks you like. This is relatable for a lot of students. Having relatable problems makes you likeable.
Just be careful to not come off as an elitist about it. Don't talk shit about cheap drinks, cause that's what other people will be drinking. Answer questions if people are curious, but don't hold lectures about fine wines and scottish whiskey (people who do this are usually the most annoying assholes at any party). And if you want to drink even less every time you're out partying - share your drinks with others if they look interested.
I dunno, this might not be a good idea depending on who you end up getting to know, but it could help you fake it till you make it I guess.
Good luck dude.
PS: English is not my mother tounge. If sentences are weird, interpret them in the most sensible way you can :)