If you are able to get the TPO ab and TG ab tests done, and they are above range, then that will make it easier to persuade your doctor to prescribe
thyroid meds.
A good thyroid doctor will treat a hypo patient clinically by testing and adjusting Free T3 and Free T4 as necessary to relieve symptoms, without being constrained by resultant TSH levels. You can get some good insight from this link written by a good thyroid doctor.
http://www.hormonerestoration.com/Thyroid.