I know that you said you are shy and socially awkward, but I’m curious - what do you do when you sit with these people?
Because I mean…simply sitting nearby some folks is not going to endear you to them. Nor is sitting nearby and throwing out random things into their conversation every so often. And if you are sitting near them/with them just not to appear alone, it’s possible they are picking up on that and it’s creeping them out. That may be why they want to exclude you.
Also, just because people have already formed a group of friends doesn’t mean they won’t let you in it, or form another group with you. Many people have several groups of friends they hang out with for different reasons.