You can try going to a naturopathic or functional medicine doctor. They are usually willing to prescribe desiccated hormones when conventional medicine doctors aren't, though there are conventional doctors that are willing to prescribe desiccated hormones. Instead of wasting time and $$ visiting various doctors, call around to endos, internal medicine doctor and general practice doctors that treat thyroid disorders and ask if they prescribe T3 medications. If they don't, you know you don't have to waste your time going to them.
Have you tried cytomel or it's generic counterpart, Liothyronine? I take Liothyronine and have good luck with it. Some of us just need a small boost of T3, instead of a lot.
You can buy any thyroid medication without insurance if you can afford to pay for it, but if you're in the U.S., you can't buy any thyroid medication without a prescription.
If you'll give us your location, perhaps we know of a patient recommended thyroid doctor in your area.
In addition, if you could post your actual thyroid hormone levels, we might be able to help you determine a course, of action. Be sure to include reference ranges with any lab results as ranges vary from lab to lab and have to come from your own report.
Some vitamin/mineral deficiencies can cause hypo-like symptoms, as well as interference with thyroid medications. If you've had vitamin B-12, vitamin D and ferritin levels tested, please post those results with reference ranges, as well.