Interesting about the iodine... would that indicate that there is something wrong with her thyroid and that could be the cause of her hair loss? Did you get blood work done to determine thyroid function? We live in Canada and I was so worried about my daughters hair loss that we ended up spending 6 hours in the emergency to get some answers. They wouldn't take another blood test because we already have one pending but they did reassure us that it's not something to be worried about unless she is having other symptoms such as: fatigue, weight loss, inactive... our daughter is exactly the same besides the hair loss. If it turns out that she is anemic or has a thryroid disorder, once started on medication the hair will begin to grow back.
Have you tried giving her iodine and silica? I think they sell those things at health food stores. I've read online that people who have started taking those minerals that their hair has started growing back...I might actually look into getting some for my daughter. Hope this helps... hugs... we're right there with you!