I feel like **** at uni; are these people even my friends?

I'm trying to get to know my group of "friends" but it's so hard. I'm trying so hard to keep the friendship. I just feel so crap and lonely.

Yesterday, Katie, Hannah and I was walking to our lecture and Katie turns to Hannah, "let's go library on this so-so date" and she didn't have the decency to include me? I was literally beside them... am I invisible or something? I felt like crying on that day.

So I made new friends and I went out with them on this party event and I managed to bump into Katie and her friend and her friend's boyfriend. She comes over to me and says, "let me hang around with you, I don't want to be a third wheel/awkward around them" - SERIOUSLY!?!?!!??!? now you want to talk to me...

Where do I start?

When I started moving in the flat, I met my fellow classmate (let's call her Katie) who I talked to over Facebook before. It was nice since she was the same ethnicity as me.
After a week, she talked to other people in our course (Of course I did too) and after several days, I missed one day (it was a full day full of lectures) and when I fully recovered the next day, they organised to meet in the library without me. I felt so left out. The day I wasn't here, they automatically become "best friends".
Every time I meet up with them, it gets awkward - it's like they don't want me there. I can sense it. Cos one time, we was walking to a lecture and I was in front of her walking towards our seats and 30 minutes later, she goes "where's so-and-so (meaning me)"... I WAS IN FRONT OF HER. WALKING IN FRONT OF HER. HOW COULD SHE NOT SEEN ME.

This recently happened as well... the lecturer gave us a task to work in groups of 3/4 and once we dispersed, She (Katie) said, "I'm going to work with Hannah (this girl in our group; we have our little friendship group in the course) and She (Katie) looked at me and said "who are you working with?" and I said "I thought I was working with you guys" and she said "Oh.." ... I mean...come on!!

I was friends with her before the course started and now she's become like this - leaving me out on this like I'm invisible. I feel so depressed. I know I shouldn't dwelll on this but it doesn't make sense... I just want to cry cos that's all the friends I've got...

Uni will be fun they said... fun... on top of that, I have social anxiety which probably why I'm hated... ugh. Can someone kill me now... I had depression before going to uni too... feels like it's coming back.

Maybe I don't deserve to have friends...