You can also get potassium iodide (KI) tablets if the taste of kelp makes you gag.

I actually like the taste of some kelp; in modest amounts mind you. Kelp tablets are a good source of iodine but the iodine is less readily available than it is in KI. But, I would take it in kelp form if for no other than philosophical reasons.

If a person suspects iodine or thyroid deficiency, however, they would be best advised to get a blood test: there are other medical issues with symptoms similar to thyroid problems that iodine won't help.
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May I walk in beauty.