Go down to the school and get that bullying sorted ASAP. Tell them that you'll hold them personally liable if anything happens to your dd if they don't act and do some anti bullying workshops. And that you'll sue. Lay it out for them. It's TOTALLY unacceptable that the nurse told her that she's the one to do all the work/ take the blame. Just boggling!
No social media - bullying's bad enough in ordinary time, but if she's being bullies it's 24/7 and she has no down time from it.
She must get a hobby. Bring her horse riding, she can muck out for rides. Nothing as satisfying as cleaning up horse shit / building stone walls.
If she's interested in animals she could get a Saturday socialisation job in an animal shelter.
Do you have a pet?
Does she play an instrument? Do any sports, draw, make puppets? Bake cakes?
She needs to meet a new group, and to socialise outside her school group, doing something constructive that she's interested in.
Failing that try her on St. John's wort for a month and see if it makes a difference. Are her periods heavy and making her anaemic? Could she be on the pill without telling you?
Bring her to the GP and see what s/he recommends if it's a hormonal issue. Have bloods taken, and refer to a gynae if necessary.
Good luck!