Even the slightest amount of iodine-caused bromide detox can poison the hair follicles and cause hair loss. If that's the issue vigorous salt loading should help. Try Dr. Shevin's formula http://www.breastcancerchoices.org/drshevin
Another cause of iodine-related hair loss is a drop in iron levels from the initial metabolic boost. Floradix has helped many and does not cause constipation.
There are people who are hyper and have goiter. That's reported in the medical literature. If Iodine deficiency impairs the thyroid you don't know which way the chips will fall.
Keep trying and let us know what works. We're always learning.