I have son that is extremely sensitive...too EVERYTHING. It is nice to know that he is very empathetic to people but difficult to see his feelings be hurt so easily. I started by teaching him how to tell kids to "stop" whatever behavior is bothering him by using a bold voice (which was very difficult for him to practice even at home with me, he just doesn't have it in him to react that way). Then we worked on me not intervening so much, I learned he had to learn how to cope and react without running and crying to me. I didn't ignore it but I tried to tell him that he needed tell the child to leave hime alone first. If it continued then I would say something to the child.
I noticed it happening around 2 1/2 years old, he is now just over 5 and it has begun to tapper off a bit. I am afraid though that some of it is just do to presonality. When he gets frustrated, angry or sad he tends to cry. Your daughter might be the same way.