I take Lugols. I get it from jcrow.com. Hypothyroidism is probably even more reason to take Iodine. Regular doctors have not been educated properly in this regard. You need to learn what the doctors who specialize in Iodine are saying about it. Here is a link to something Trapper posted about this on the VWT forum-
Educating people on Iodine supplementation is something I'd rather not get into, especially when there is a forum at CZ that specializes in it. VWT can do a lot better job of it than me. I've only been taking it for a year. All I know is it sounds to me like therapeutic supplementation with Iodine would be nothing short of miraculous for you.