We need lab range usually lab range vary from lab to lab.
Exist others thyroid treatment like the combinaion of levo/cytomel (T4/T3) or dessicated thyroid gland tablet like Armour or cytomel only (T3 only). But T4-only or levo alone not necessary work for everyone. If your physician is orthodox(the majority of the physician are orthodox) you will have to seek another physician because orthodox physician arrongantly believe that the hypothyroidism should be treat with T4-only.
Adrenal fatigue or adrenocortical deficiency (which I prefer call it) could be diagnosed using a cortisol blood test. If your level are low or mid-low a AF should be suspected.
Have you checked for Hashimoto's thyroiditis? It's a very common type of autoimmune thyroid disease. It could result in fluctuating TSH values as when the thyroid is damaged, more hormone temporarily floods your system. Your doctor would need to test for both TPO and TgAb antibodies to see if you have Hashi's.
Some suggest that there is a link between any autoimmune disease and celiac disease- the theory is that when celiac damages your intestine, undigested food and other foreign stuff slips into your veins. As your body builds defenses to attack the invaders, it happens to build defenses against your own tissue. I read that eating gluten aggravates Hashimoto's thyroiditis in particular.
If your joints are hurting, you might want to have your Vitamin D level checked. Mine was very low, and when I brought the level up (10,000 IU of D3 daily), my joints felt better!
As for adrenal fatigue, it still seems controversial. Yet I wonder if there isn't a connection to the adrenals somehow. On the Johns Hopkins Autoimmune Disease Research site, they list Polyglandular Autoimmune Syndrome - 2 of the 3 types involve adrenal insufficiency.
Without ranges, it is hard to tell (TSH is standard, the others are not).
Weight gain points more to hypothyroidism or to, if it is an issue, elevated cortisol, not low, but you have no tests listed that are really directly for adrenals.
AF is a not a MD accepted diagnosis. You can have an issue, but your doctor needs to test further for it. As well, thyroid meds take a while - up to 6 weeks - to really kick in. Did he do antibody testing as well? Ultrasound?
Also my globulin is 37g/l which appears to be out of the normal range