I'm no doc but t3 and t4 being so high might mean your thyroid works just fine in producing them using Iodine in your body. TSH is pituitary hormone that tells thyroid to make more t3 and t4, but obviously pituitary is working fine as it has cut its output signal of tsh so that thyroid doesn't make any more t3, t4. I would venture a guess that if you stop taking Iodine everything would tend towards normalcy.
and try not to worry, usually things aren't as bad or as good as they seem at first.