I (19M) got black-out drunk and woke up with a friend (20F) who now thinks we're in a relationship which I don't want.

I feel like such an idiot about this but I really need advice about what to do. I know its my own fault. TLDR version is I (19M) got very drunk with a girl in my friendship group (20F) and woke up with her with no memory of what happened but apparently we slept together and now she thinks we're in a relationship.
I'm trying not to make this too long and hopefully it makes sense. To give you some background, I'm a uni student and I have a group of friends who I spent most of my time with. The girl I'm posting about is one of the people I'm less close with in the group if that makes sense. I've known her about 1.5 years but she's childhood friends with several of my friends so they are probably closer to her than me. She also lives with two of my closest friends. I knew she was interested in me because she has tried to make a move a few times and has asked me out in the past but I said no. I wasn't interested in her other than as a friend. I'm also avoiding getting involved with anyone due to some confusion I'm having but I haven't discussed that with anyone whatsoever so most people assume I'm just shy which is also true.
I recently went out with some of my friends and this girl was there. Not many people stayed out and at the end it was just me and her at a bar. I don't remember how that happened but I know in the past some friends have encouraged her to make a move because they think it would be good if we got together so maybe it happened like that on purpose. I don't normally drink much and I was extremely drunk. I barely remember the part of the night when it was just me and her and I don't remember going home at all. When I woke up she was there and we were both naked. She said something about how she was happy we finally got together and at the time I didn't know what to say because I didn't want to admit I didn't remember and regreted it because that would be hurtful. I was also extremely hungover and confused. She wanted to hang out more that day but I convinced her to leave because I was so hungover. I have avoided seeing anyone since then.
Ever since then she's been talking like we're in a relationship and I suppose in her view we are even though it's not what I want at all. This all happened around a week ago and she has been telling everyone we are together and our friends are all happy about it. I have no idea what to say which I know is weak but I don't want this relationship and I don't want to hurt her by saying it was a big mistake. I don't think there's anything I can do that won't end up with me being the bad guy and probably losing most or all of my friends. I've been trying to avoid everyone but I can't do that forever and she is pushing to spend time together which I understand since she thinks I'm her boyfriend.
I'm probably just going to be told I need to grow a pair which is fair enough because it's true but I really need advice. I'm a socially awkward person and this is the first time I've had close friends. I don't know how to deal with this scenario. I had a dream last night that it didn't really happen and I woke up feeling so relieved then I remembered it was real and I feel so hopeless now.


Source.