I supplemented with iodine, in my case Lugols iodine, as I had other issues as well due to Iodine deficiency. Hv recommends kelp and other Iodine rich foods, which is also fine with me, but Lugols (and the companion supps) worked for me. I was extremely Iodine deficient, among other deficiencies, including magnesium, potassium, vitamin B (all of them), and others.
I do not have hypothyrodism any more, and I have not been sick at all for more than 18 months.
Hv has had a lot to do with this, his advice is invaluable :)