Chill. You're going to be fine. Like you said, your self-esteem has had a knock, plus you're recovering from surgery so you probably feel pretty crappy. It's likely you're seeing the worst in things at the moment, but just because you're picturing all sorts of awfulness doesn't mean that's how things will turn out.
First off, it's like six weeks until Freshers' - I'm no maxillofacial surgeon but that seems like a decent amount of time for a) the swelling to go down a lot and b) you to get a lot more used to dealing with random dribbling and whatnot. I bet things will be a lot better by September so it may be far less of a problem that you're picturing.
Secondly, when did you last decide you didn't want to be friends with someone because they had a puffy face? I'm guessing never; as is the case for more or less everyone. I'm sure the vast majority of people will be sympathetic to your situation, not make fun of you. You might want to think about how much info you're comfortable sharing with flatmates and people you meet, so they'll appreciate the situation.
And if you do happen to come across anyone who's an arse about it, well, that's because that person's an arse. It's not a reflection on you. Have a nice cutting response prepared in case anyone does say something unpleasant - something like saying "Wow. That was really rude" and going back to whatever you were doing without missing a beat. I don't think you're likely to need it, though; it's just something to have up your sleeve.
And, if you're feeling a bit fragile at the moment (which it sounds like, from your post) then whenever the events listings go up for Freshers' Week you might want to plan some low-key things to be doing where you feel like you'd be comfortable. Maybe Volleyball won't seem like a great plan but you'd like to see a film at Campus Cinema; maybe go hang out with KnitSoc rather than try Kung Fu that week. See what takes your fancy, there'll be loads.
Hang in there (I was going to say 'chin up' but I thought it might sound like I was taking the piss!) - you'll be fine. Hope you feel better soon.