I doubt that losing hair was due to iodine intake. In fact, a number of articles mention possible hair loss due to iodine deficiency.
I'm pretty sure it was because the massive amount of toxins it released from taking the iodine. I've seen actual studies that show that iodine releases mercury and it doesn't effectively chelate mercury so redistribution risks from it are real.
It is hard to tell the difference between healing reactions and redistribution in the case, so I think caution is very necessary.