Having Trouble Finding A Thyroid Medication, For Hashimoto's, That Is

Having trouble finding a thyroid medication, for Hashimoto's, that is allergen free. I've been taking Tirosint because of Celiac, which has led to corn allergy. Insurance, no longer wants to cover Tirosint and suggested; Unit Direct (which I can not get to come up in a search), it comes up as Unithroid, which has corn starch. The other suggestions; Levo-T, has sodium starch glycolate (could be rice, potato, wheat or corn - haven't found the pharmaceutical company in a search, yet. I do know, because I've had to do wll my own searches, thus far (4 yrs), that WP Thyroid/Westhroid/Thyroid P are allergen free, however, convincing my Endocrinologist is the next big step. He took me off Nature-Throid upon my first visit. And, for the life of me, I can not understand how Hashimoto's (hypo/hyper thyroid) can even be treated other than just a low dose for stability(Endocrinologist has had me on 100mcg & 88mcg of Tirosint and pushed me to Hyperthyroid (severe Rapid Heartbeat). I've currently regulated it myself w/ 1 tablet Mon, Wed, Fri & Sat., the Rapid Heartbeat has gone down to just palpitations on Sunday after the back to back Fri/Sat. And how do you treat this if you have Adrenal Fatigue on top of it. Is there no medical testing for the ENTIRE ENDOCRINE SYSTEM? Sooooo frustrated! Thanks for liistening/reading and any feedback you can offer.