@whitefr0st : I would talk with a counselor since you have that option. They may have specific info on techniques to use to quiet your anxiety (biofeedback, etc), and suggestions on where to find others in your same situation.
You might also try planning a get together for the club group. Perhaps many of them are also having difficulty making friends. It doesn’t have to be an elaborate thing, if there is something on campus that you want to do, ask the group if anyone else wants to go too. Keep asking even if the first few times don’t get any response. Perhaps those people are shy. Or on limited funds.
You may not have a lot of free time, but volunteering at something that is meaningful to you would be helpful to others and you could meet like minded students.
Also, see if there are any social groups that are doing something that you would like to try, such as ballroom dancing, painting, a foreign language group, a cooking group, a group sport (I wish Quidditch had been around when I was in college ;), a reading group, etc. Try something new.
Keep on looking, you will find your tribe!