what really works and is cheap to make alopecia go away?

The only thing she can do is see a dermatologist. There's is nothing sold over the counter that takes away alopecia. It's very hard for an 11-year old to put up with this. I feel for her.

There is no "cure" for alopecia.  Some people find that cortisone injections in the scalp work to stimulate hair growth.  Those are painful and could be expensive, though.  But even if the hair grows back, there is no way of knowing how long it will stay.  The best thing to do is talk to your doctor.  And if the hair still doesn't grow back it is a good idea to go to a therapist or counselor because alopecia can cause a lot of emotional pain.  Visit www.naaf.org and see if there is an alopecia support group near where you live.  That will help tremendously.  Good luck.