Iodine from Seaweed

I was taking iodine supplements for my thyroid, but was wondering if seaweed products would help as well.  I am all for as natural as possible.  I'm not a big supporter of medicating with prescription drugs unless necessary and I'd love to give enough support to my thyroid that I could possibly reduce my thyroid dosages (assuming my thyroid isn't totally useless at this point).

I've been hypothyroid with Hashimoto's Thyroiditis, goiter, and nodules for more than ten years now.  What an emotional roller coaster ride!