You've gotten great advice already. I thought I'd share what my fearful DS is like at 15 years old. Like your DD he was very verbal, sensitive and was afraid of quite a few things but most notably noises and other people including other children.
At 15 he is still sensitive to all of this, but, to put it shortly, he is also absolutely wonderful and very happy most of the time. He is very choosy about his friends but when he makes friends they are for life and he has no problem socializing with children that are respectful of him and others. He has no patience whatsoever for jerks though and funnily enough stands up to them very well. I'd never have thought so when he was a toddler.
He doesn't love new situations but surprised us this year in trying the excellent soccer junior varsity team of his high school and making it and fitting in just fine with the other players even if he still has the tendency to stay a little ways off sometimes.
I've had many many conversations with him through the years about his fears and need for solitude and lack of socialization and it took me until this year (!) to realize that he was indeed just fine, happy and that he was making his life the way he wanted it: very good true friends, sports that he love and respect for his need for solitude.
I'd also add that he is extremely gifted. His teachers have been astonished from an early age and we put him in a program for gifted children ( that I noticed, are often socially awkward ) where he did very very well. He likes to be around people who want to do things and learn and not just "get by".
He did have a period from 9yo to 13 yo where he would sometimes get depressed and would say things like " I want to disappear", " it would be better if I die". Especially during middle school. His school was small, we had particularly chosen that one for its smallness thinking he'd like it better. It was a big mistake. If you didn't like some people it was difficult to avoid them and there are plenty of jerks in middle school. His high school is huge though and he loves it and has made a lot of new friends there. I guess there is a much wider pool of people.
We never thought of getting him help since we seemed to do a good job by ourselves. And really I think his behavior is due to his giftedness. It's difficult to glide through life as if unaware of dangers when you have a very analytical mind. If on top of that you have a great imagination, well, I wonder what your DD actually sees when there is a crack in the sidewalk... I was like that too...I'm still like that but I can now reason with myself. I took me time though.
I'd just keep talking, and talking and talking about her fears and feelings :). Also we did not avoid activities because he was afraid but never pushed him either. If he was afraid of the animals at the zoo but still enjoyed part of it, we'd go and he'd stay in our arms the whole time talking about what he was seeing. He was not upset whatsoever to not be running around like the other kids. If he had, it would have been another story.
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This is so incredibly lengthy...sorry! It's just that I have worried so much about this for so long. I hope it helps.