Loads of people don't know each other unless it's a very small course. It doesn't feel like that though. The flatmate thing is probably a little different, but they are just flatmates.
The thinking everyone has met everyone and all friendships are locked in is a normal thought taken from small social cues that your social anxiety has taken and magnified 10x.
If you took a bunch of strangers with anxiety and put them in a room with some people that had met once before what would happen? You would get people over reading the situation and looking for other 'new people' and then jumping to conclusions that everyone else knew each other apart from those who actively identified themselves as 'new'. If someone started saying hey we're all new here some would physically recoil and move into smaller groups. Afterwards some of the new people would say that they knew straight away that they wouldn't fit in and it's so frustrating how everyone else knows each other and they won't come again.
The above scenario happens in real life of people of all ages with anxiety. The difficulty is overcoming those tiny cues that we over read.
It's socially acceptable to go to events at uni alone.
With the society I would book a day in your diary to work up to going. Do things that help, maybe the week before walk past the event and see who goes in, where it is, everything to try and make it easier. Then go the week after. If you don't go (try) then don't beat yourself up, try the week after. Have a plan for leaving early etc if it doesn't work out. An excuse.