I had pain in my thyroid area periodically when I started iodine.
For me it was a sign to back off for a few days.
OR, to change the type of iodine. The ones that caused the most pain was the detoxified version aka Cayce (similar to nacent iodine). And the magnacent; the little I tried, added to SSKI ; gave me pain.
To compare with kelp; never gave me pain, but never any benefits either.
Increasing the selenium always helped with the pain, within a day or two.
To let you know the next step is difficult; as we are slightly different in how we react on Iodine / co supplements. Answers are mostly based on our own experience, and this is my two cents:)