You need to have antibody testing done to see if you have Hashimoto's or Graves Disease. The tests would be TPOab (thyroid peroxidase antibodies) and TGab (thyroglobulin antibodies) for Hashi's and (I *think*) the main one for Graves is a TSI test, but I'm sorry I can't tell you what that stands for, as I don't have Graves and am not real familiar with it. A thyroid ultra sound would also be helpful to determine if you have a goiter and/or nodules.
If the range of your FT4 is anything near the one my lab uses, your FT4 is too low at 0.5. I would suspect that your FT3 might also be too low, but since that wasn't tested the last time, there's no way to tell.
It's very possible to have a normal TSH, even if your actual thyroid levels are off. I'm not a believer in even looking at TSH until the very last thing because it's a pituitary hormone and is not necessarily indicative of your actual thyroid levels. For instance: *my* TSH runs at only 0.01, so anyone adjusting meds based on TSH would decrease my med (yes, my doctors have done that) and send me back to hypo he// (yes, THAT happens too - in fact, I'm just "coming back" from a hypo crash for that very reason).
I suggest that you find a doctor who will look first at your symptoms, then at your actual hormone levels (BOTH FT3 and FT4), and lastly at your TSH -- the idea being to begin and adjust med to alleviate symptoms, not just get the lab results into the "normal range".
You might also want to have your vitamin b12 levels tested -- b12 deficiency can cause a lot of the fatigue you mentioned, along with tingling/numbness in the hands, feet, legs. I turned out to have a combination of b12 deficiency AND hypothyroidism, so was getting a "double whammy".......I'm now on both thyroid med and b12 shots and now that my thyroid med is pretty much adjusted, I'm feeling better than I have in years.
Its good to know if you convert to T3, as you seem to understand the possibilities are not 'standard' with all of us. They dont test to save money, I would suspect, even though the odds are against some of us.
You should seek testing for autoimmune thyroid issues.
In your quest, do not rule out other things that mimic hypo thyroid, gluten issues, digestive (whole body) bacterial overgrowth including Candida.
Your tsh seems to vary, have other hormones tested ever? - they 'pull' on each other. Adrenal levels are tied into this as well (the 4 point, 24 saliva test is best).
Can you post the reference range for the FT3,FT4 ?
If you are treated correctly then TSH and FT4 are adjusted properly then your FT3 supposed to be fine except some cases of conversion problems.
Some times the TSH is in normal range but you still have autoimmune disorder ,to know that you need to ask for anti TGab and anti TPOab .