I forget on how university age works in the UK. Are you 18? If you're 18 then your parents have no right to access your medical information and you would be able to go to your GP for assistance without fear of them interferring (they could only do that if you signed a waiver consenting to allowing them access).

I'm sorry that your friend led you on like this. She probably underestimated how deeply you would respond to that sentiment. Maybe she doesn't understand how a healthy relationship should work either.

Regardless - it is NOT your fault. It takes two to tango and she made mistakes in this relationship.

Friendships are hard when you don't have a safe history to rely upon to help guide you.

I'd give the university counsellling a shot anyway. You could always bring in a letter the first time describing your challenges so that they could know what you're needing help with even if you freeze up and can't talk at all the first time. If nothing else, you can use it as practice each time to see what you can push yourself to do.