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I met a girl on a night out, I need some advice

I just started my first tear at Uni and a couple of nights ago I went on a bar crawl with one of the societies I've joined. I met a second year girl who is also joining the society for the first time We started talking halfway through the first bar (which was technically our society family house), got on really well and had a lot to drink together. I remember everything up until and hour or so into the third bar and we were getting closer and closer, dancing and having a great time. I'm sure we were about a kiss at one point but a big group of guys barged between us and separated the closeness. It was not long after that that my mind goes blank and my next memory is of walking to the next bar with the society talking to one of the guys in charge, I didn't see her again for the rest of the evening despite spending most of my time moving around the group looking for her. I'm terrified I did something inappropriate and scared her off during that time of blackout, the other people we were with said they don't think I did anything but they were pretty drunk too so I could have done, they also don't remember when she actually left.

I've never been in the "meeting someone on a night out" situation so I don't really know where to go from here which gives me a few questions

1. Do I even bother contacting her again, I have been guilty in the past of thinking someone is far more into me than they actually are but something felt different about this

2. I was planning to ask for her number on the way to the 4th bar but for obvious reasons I wasn't able to. She doesn't have Facebook (or at least I couldn't find it) so the only way I've found to contact her is through the University email system. That seems like a bit of a strange thing to do to me, what do you think? Also, what should I say in the email?

3.The next time I see her should be at the next society meeting but that wont be until sometime next week which feels like I've left it a bit too long. Should I say something different because it's been left a bit longer and it's face-to-face?

4.At one point while we were walking and talking (I can't remember exactly what we were saying but I think I was just doing my best to make her laugh) she just suddenly said "You're really sweet" and I said "Oh, thank you very much" and we carried on talking. Is that a good sign or more of a lets-be-friends sort of thing. It was an hour or so before the "almost kiss" by the way

She was a really nice, funny person who I'd love to spend more time with even as just friends so any help would be greatly appreciated.