Can I see your labs? I'm betting your doctor either didn't look at everything or he/she doesn't know how to properly read the results.
Insist that your doctor check T3, FT3, RT3, FT4 as well as thyroid autoantibodies TPOAb, TgAb, TRAb, TSHR Ab, and TSI.
Note that after Iodine supplementation, TSH will become completely unreliable in terms of using it as the diagnostic for thyroid dysfunction. (Some see their TSH skyrocket while others see their TSH fall.) But it's still interesting to check it anyways for data compilation purposes.