Just want to weigh in, I agree with everyone here. I also found that increasing my thyroid meds too high gave me an "oversensitiized system" which sounds like what you are experiencing. I have HypoT and Adrenal and have been successfully found the right treatment combination with Naturthoid (2.5 mgs/day), and Hydrocortisone (27-30 mg/day).
Though my TSH is .01 (almost totally suppressed) but I feel better now than I ever and my HypoT symptoms are gone.
If you are interested, here is my story along along with some good before and after photos...