DD is nearly 7 and has always been slightly different (to friend's children that I know). She never ran off anywhere such as shops/roads/parks when younger, always holds your hand, can sit quietly and play for ages, we never had to use child locks or anything - if you told her not to touch she wouldn't, only ever really had 1 tantrum through whole life. Hates loud noises, screams if one of our cats goes near her, won't go upstairs on her own as she seems scared, same with the bathroom, always wants someone to go with her.
She has a very strong 'right or wrong/black or white' attitude and is very into telling other children when they are being 'naughty', we have tried to dissuade this. She gets very upset if she feels someone has done something 'wrong' to her, cries and is inconsolable. She says that I and her step father 'shout' at her when we really don't at all. She also says we're being 'nasty' quite often when we're merely correcting something she has said or explaining something to her.
This is all quite wearing and now its started to transfer to school, she constantly comes home and says she is being bullied at school and that no one will play with her. With further questioning it is usually that they wouldn't play the game she wanted or how she wanted to, but to her it is real and she is devastated - crying, saying she wants to change schools etc. I can see from their point of view that trying to play with such a 'rigid' (?) child who tells tales 
We've tried reading age appropriate books about being a good friend/getting along etc, tried telling her not to react when things are said to her (she is a bully's dream in terms of reacting), tried all sorts but nothing seems to be working.
Any ideas? How can we make her less sensitive? Should we even try anyway to change her? Has anyone else got dc like this?