Poor dude. You remind me of myself as a little kid. You're going to have to learn to stop worrying incessantly about approaching people. This might come easily once you get confidence but really, you're going to have to go for it, take the risk of making a fool of yourself.
Some people are born naturally confident and don't need to make a fool of themselves but unfortunately, the vast majority of men, sooner or later, have had to embarass themselves completely to learn to be comfortable approaching women. There's no secret to it.
Yes, ask for the e-mail. The trouble is, there's no way to tell if she liked you and even then, so what? What you have to realise is that girls change their mind contantly. You're the timid, introverted type who focuses on girls for long periods of time so you assume that if a girl liked you once, then she must like you forever. Not so, my friend. Who knows, maybe that day, she felt interested in having a bit of fun and THAT was your chance. It doesn't mean that she was crazy about you, that she loved you. Maybe because of your reactions, maybe simply because her mood changed, as girls' moods do, the way she felt then, disappeared right away.
You're making films in your head, thinking that just because a girl showed some interest in you once, she is thinking about you constantly. I can't say for sure but what was most likely is that she was a bit interested then and that was your opportunity to really make her like you. THAT was the opportunity, when you were there. Sending an e-mail is not the same, as you won't make her like you, the way you could have, if you'd tried your chance.
Again, don't mix up a LITTLE interest, at SOME point in time, with "Oh my god, she really likes me!". You're just imagining things.