Primal doesn't necessarily mean low carb. Eat for nutrition first, the most nutrient dense foods. If you can afford or get grassfed meats do it. Wild caught fish is better than farm raised, not the same for shellfish though which is equal to wild. Look into farmers markets, and urban foraging in your area. Someone more versed on Thyroid issues could probably give you an idea whether supplemental iodine would help your issue.
I suggest you check out the Perfect Health Diet, which is endorsed by Mark Sisson (he wrote the foreword). No need to fear the carbs, but you have to pick the right ones ("safe" starches, fruit) and avoid the bad ones (grains, legumes, sugar).
Good luck, I think you should see considerable success for your issues if you follow the PHD approach.
If you are getting a rash from Iodine supplements, that could be an allergy. Try finding a different form of Iodine or none at all. Consider going to an allergist.
Thanks, FlyingPig! I will check that book out!
Workinprogress, the issue for me is an excess of iodine causes the rash. I'm not allergic to it in general, thankfully.