You might search for the half-life of Iodine supplements.
The results may be different for 1mg doses of supplements rather than US RDA level supplements.
Learn about the various thyroid tests. TSH is very commonly used by insurance doctors; however the work horse thyroid hormone is T3.
Even if your test comes back negative, you may like the effect of related supplements--iodine, selenium, zinc, glandular supplements, maybe ashwagandha, etc.