I suspect that this friendship isn’t the only instance in which you feel anxious and uncomfortable. People become anxious to varying degrees based on their temperament (which is, in part, genetic) and it can be upsetting, and hinder their performance both academically and socially.
You sound very smart and insightful, and seem highly motivated to change. Given these factors, you probably would benefit from some short-term therapy (not psychoanalysis) to help you deal with your anxieties. I suspect that this will not only help you with your friendships but will carry over to other aspects of life. Since you are on a college campus, you can see whether the student healthoffice offers some kind of screening and can provide short-term therapy like cognitive-behavioral therapy (CBT).