Socially rejected in banking? How to make friends?

I'm a junior and have an internship with a BB for this summer. I worked hard at networking and interview prep and my parents are proud of me. But I can't get over the anxiety of making friends at the office this summer, as well as after graduation.

Even though I somehow made it through the interviews, I have struggled with people for most of my life. As a kid, I was bullied. In college, it hasn't been much different. I rushed frats hard but got no bids. I was socially rejected by my dorm hall because people thought I was fake and too intense. Last summer, I worked at a firm with 3 other interns. We hung out together 4-5 more times. I didn't make any major social blunders and we honestly had fun. However toward the end, the other interns became incredibly close with each other while I found myself excluded. **It seems that I am always choosing between being restrained and coming across as cold and distant, or being vulnerable and coming across as inappropriate. **

I've met some of the interns and analysts I'll be working with summer and they are great people. I don't want to fuck it up and will do anything that will help me make friends and learn how to strike the right balance between restraint and vulnerability.

Does anyone relate to this? If you've been able to ramp up your interpersonal skills and make friends after college, or are in a similar situation, I would love to hear your advice/experience.