Don't lose hope...which I know sounds stupid, when you feel lousy. You may never find a Doctor to, 'work,' with you. Doctors are taught wrong. Only YOU know how YOU feel. Don't let them tell you how you feel. I personally went through 10 doctors. I always left in tears and hopeless, because they wouldn't listen to how I felt.
Research is going to be your only friend. You have to be your own advocate and Doctor. Learn the science behind the endocrine system. Don't believe everything you read either. Some, 'science,' is tainted by these same ignorant Doctors who are keeping you sick. They hear the same information long enough and they start to believe it, without doing their due diligence. I suggest reading medical journals, from before synthroid was brought to the market.
You have to also work on your adrenal health. (Try to find a doctor who will even admit their is a problem, without an adrenal crisis, like Cushings, or Addisons.) Your body needs cortisol, to convert T4 to T3. Without it, T4 will convert to RT3. High cortisol isn't good either. It will suppress your TSH and also give you hypo symptoms. You will need a 24 hour saliva cortisol test, which unfortunately, you will probably have to pay for yourself. You will also need your DHEA tested, RT3 and vitamin deficiencies.
Stay away from gluten!! No cheating even a little bit. Anyone with thyroid disease must avoid gluten like the plague. The protein in gluten, resembles the protein in your thyroid. When your body makes antibodies against the gluten, those same antibodies attack your thyroid.
You need iodine therapy. The, 'T' in T3-T4 is actually iodine molecules. T4 has 4 molecules of iodine-take one away and you have the active thyroid hormone T3.
"Incomplete conversion of T4 to T3 can also lead to low thyroid symptoms. T4 receptors in the body have not yet been identified; therefore, T4 needs to be converted in the peripheral tissue to the more active thyroid hormone T3 in order to relieve low thyroid symptoms. T4 is converted into T3 by removing an iodine from the T4 molecule at the 5’ position [Source: Paoletti]. Factors such as nutritional deficiencies and medications can inhibit this conversion. Nutritional deficiencies such as iodine, iron, selenium, zinc, vitamin A, riboflavin, pyridoxine and B12, along with the use of certain medications including beta blockers, birth control pills, estrogen, iodinated contrast agents, lithium, phenytoin and theophylline can inhibit the conversion of T4 into T3. Other factors that can cause this inhibition include aging, alcohol, alpha-lipoic acid, diabetes, fluoride, lead, mercury, pesticides, radiation, stress and surgery [Source: Brownstein]."
This kind of information is easily found, if you just search. Again, don't take my word for anything, do your own research and make up your own mind. BTW, you can find governmental websites with this information. Also, look up the Scottish Thyroid Petition. Good Luck.