Patients with symptoms such as yours (feeling worse with higher doses of Synthroid) often have a "REVERSE T3 SYNDROME" where the Synthroid gets converted into "Reverse T3" that is biologically inactive (it has no effect in your body. In addithion the higher dosesof Synthroid suppresses your own thyroid's ability to make ACTIVE T3 by lowering your TSH.
Switching to Natural Desiccated Thyroid (Armour Thyroid, Nature-throid, others) could solve this problem as NDT has active T3 in it, not just T4.
The clinic has not tested the reverse T3 ratio, only the tsh, free t3 and free t4. Prior to the hashi's, my tsh had historically tested 1.8-2.4. I go to a military health clinic and I don't believe the NDT is an option for me as I think they only stock synthroid. In addition to the my tsh now down to a .64, which is really low for me, I have also had shortness of breath, fatigue, headaches, memory fog, and hair loss. I don't think I can get the NDT, but could ask for the additional t3 supplement drug, however with the free t3 being in the "normal" range, I doubt they would give it to me.
I have patients who are active duty, in the reserves, or veterans, who "leave the base" to see doctors not part of the system, to get the care they need. The military won't do cosmetic surgery or Botox injections for wrinkles, but does not prohibit their soldiers (or their families) from doing so privately, as long as it doesn't adversely affect "service readiness". Having less brain fog, etc., would only improve your service readiness, so I don't think your commander would object to you getting a second opinion off base. The military might pay for that care, but like a lot of patients whose HMO won't provide "quality enough" care, you might have to take matters into your own hands.
I asked the clinic to test for the RT3 levels and they said that if needed they will give me a script to purchase Armour thyroid off base. They put me back on the 75mcg of synthroid and will test again in 6 weeks to see how my levels are and check the Rt3 ratio. So at least Armour is an option for me if needed. Thanks for your advice and I will let you know how it turns out.