Yes, it's not only entirely possible but probable that your tests come back normal, yet you could have undetected thyroid problems.  I do !!!

I just checked with my endocrinologist last week and she said everything was fine.  Now mind you that I have a pretty visible goiter and I'm very symptomatic.  Of course the reason I go to her is because at some point it's good to know if one has developed Hashimoto's, Graves or some other such thing, but as far as expecting her to detect minute dysfunctions, I would never give a conventional doc that much credit.  And yet, at any level, the thyroid gland can make us feel like garbage if not working properly.

Once armed with the knowledge that nothing severe is going on, I'm free to continue on my own healing path,

So if you sense in your knower that your thyroid is not as spiffy as it ought to be, by all means look into iodine.  In a few weeks I'm going to start taking Fucoidan (sp?)  You can Google this and see if you like what you read. (....Google will correct the spelling for you)

I have learned to distinguish between what I need to get from docs and what I won't let them touch; the sorts of tests that point out to the possible existence of major dysfunctions, and the things that they don't even acknowledge exist or believe in (think parasites, liver flushes, candida overgrowth, etc., etc.,)

So just go ahead and follow your instincts and supplement and cleanse.  Just proceed slowly and see what works for you, and above all, study and research all your options extensively.

Bon Chance.  :-)