Hi; ideas that comes to my mind is to change brand of iodine, or change the way you take it. Take the Iodine in vit C/ juice if you dont already.
Increase selenium for a while?
Pausing Iodine if the detox" is too bad; but since good results I wouldn't quit completely. Try 3 days on, 2 days off or something like that.
Also consider any change you may have done with diet or supplements (herbs) that may have caused it. It happened to me the first difficult year of supplementing iodine.