I went through my entire first degree not talking to anyone or making any friends. I had no idea how. Now I can even though I am older than all of them. It's more listening than talking, and being subtle, making eye contact, smiles and opportunities for the other person to respond. Also, good to have specific goals. My goal is to have someone to talk with about class material and projects, exchange email with someone in case either of us misses a class, and ideally have someone to study with for at least the final and maybe also the midterm. I have never succeeded on that last point, the midterm. Once you have specific goals, you can tailor your behaviours around that. Be friendly, but give people a lot of space. There are books about interpersonal communications that give good tips. I liked some by Leil Lowndes - very concrete, yet accurately tells you what context it would be okay in, like levels of formality. Then I practised those behaviours. But observing and listening are key, instead of worrying a lot about yourself. Paying attention to the other person. I feel I am undiagnosed autism spectrum, and this has ruled my life because of the tremendous effort required to come out of my shell as they said in my first grade report card. I have gone through what you are going through, I think, including a bunch of social anxiety in the past as well.

Feel free to PM me if you wish.