Despite (or maybe because of?) your avoidance of doctors, I'll recommend a full blood workup, at least to establish you don't have any parameters that might be red flags, especially any potential thyroid issues.

IIRC we don't need much iodine (trace amounts) but we certainly do know the effects of iodine deficiency. I eat fish at least weekly, and like nori snacks, so I don't give it much thought.

Salud!
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--Rick