There are many people who take thyroid medication in various forms while on iodine. I switched from Armour to Naturethroid to ERFA due to last year's shortages of natural dessicated thyroid.
I'd recommend that you check out the Iodine Yahoo Group. Steph, the moderator, is very knowledgeable about thyroid meds and iodine. The group is very active.
I'm not sure there was much point getting bloodwork done a week into Iodine supplementation. Iodine can cause an initial transitory spike in TSH that can last for 6 months or so. It doesn't mean it's a bad thing. Plus, it's going to take a while for your body to adjust and heal. It's not going to happen overnight.
Did you get bloodwork done before you started iodine? Would need to see Free T3 and Free T4 plus lab ranges.
You definitely need selenium for the thyroid along with your iodine plus the other companion supplements.