If you have low cortisol levels that needs to be resolved before even starting on thyroid med. Most likely you will need to start on hydrocortisone several times a day, along with DHEA-S, to counter any unwanted side effects from the cortisol. Being low in cortisol, you probably should also request to be tested for other hormones, like progesterone, estradiol, and free testosterone.
If you are below the low limit of the so-called "normal' range for T4, along with those symptoms, that is a strong indication of being hypothyroid. The ranges for Free T4 and Free T3 are far too broad to be functional across their entire breadth for many people. A good thyroid doctor will treat a hypo patient clinically by testing and adjusting Free T4 and Free T3 as needed to reieve symptoms, without being constrained by resultant TSH levels. Symptom relief should be all important, not just test results.
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