This is my daughter. Are you sure you're not my secret twin sister?
DD is almost 15 and is exactly the same: clever, pretty (think Harry Potters's Fleur Delacour), sweet, kind, but painfully shy and has no real friends. So shy that her Latin teacher has admitted that teachers forget about her in class, At Christmas she was left out of the form's "secret santa" and she is only invited out by one "friend" who, I suspect, is doing this as DD is her mum's charity case. I don't know what to do for her upcoming 15th birthday. Last year we took her and 2 friends to Harry Potter studios and her friends paired up and disappeared and DD was left crying on her own.
We are absolutely definitely changing her at 6th form. She plays the violin but I am also going to start her with 1-2-1 singing lessons so that she has to learn how to project her voice: hopefully this will mean that she is more confident about speaking up.
I think she will be fine at university and also your DD will be fine at university. She will be with more like-minded people, ie choosing a particular university, then choosing a particular course. All this is self-selection and thus will weed out those who are completely uncompatible.
Imagine going round a supermarket and having to be friends with everyone (I mean everyone) in there, because that's what it's like in school. My son will talk to anyone, but he is quite superficial. My DD is more introverted and deep. So again, by natural selection, some people will have more in common at the organic hummous bit rather than the own brand frozen sunday lunch on a plate bit. This is a bit of a weird metaphor but might help.
One last thing, I wouldn't normally recommend a website but if your DD likes creative writing, check out movellas.com - it's an online forum where you can post stories and other people comment on it. DD doesn't know that I've snooped on her page, but the support and kind words on there have brought a tear to my eye.