Hi, i dont know if this would help or what, but, since i identify with what happens to your daughter, I armed myself with courage to write a post about it

(been around since 2009, registered in 2010 but never got the courage to write xD).
I have the same problem you described, and been having it for quite some time (years). I’m 20, and it’s quite difficult for me to have a good night sleep unless i play football (soccer) long enough for me to be completely exhausted and “pass out” in my bed.
I’ve always been the top student in my class, now in college studying Computer Science and i still am the smartest guy around.
I have the same problem you described, I cant go to sleep because my mind is often too busy to shut down.
I’d recommend you take her to a doctor, I didnt go to one and still have the same problem

.
As for being bullied, i’m a man and i understand that bullying a girl is a very different thing, i think i never was bullied because even though i always was the youngest in my class, i always was the biggest and I never let anyone pick on me because i was shy (and i still am) thanks to superior body strength

. I always had trouble fitting in, i went to a private catholic school (never fitted in bcuz my interests never were the same as the other kids (everyone wants a toy for christmas when ur 5, but i actually asked for history books)), then moved to a public highschool (impossible to blend in a extremely poor and knowledge repulsive context) and finally, i earned a scholarship for a Catholic College (best university in my country) where i thought i would fit in cuz i thought everyone would be more like me and i was wrong.
As for going to a psychologist, i went to one who diagnosed me and said sincerely that she thought she might help me with my social skills (i cant express myself cuz i’m extremely shy though i have no disorder like asperger or anything) and solving that might help me achieve peace to sleep and a better concentration to study, but she obviously couldnt help me solve the other problems (math, politics, economy, education, etc) so i stopped going bcuz that’s just 1 of the problems that my mind tries to solve, and solving one but leaving other issues unresolved wont help.
Well, dont know what else to say, just, try talking to her and take her to the doctor.
See you and good luck with that, i’ll pray for her,
Sincerely,
me.