Is TSH and FT4, the only things your doctor is testing for thyroid? You should be getting the FT3 test, as well.
Please post the reference range for the FT4. Ranges vary lab to lab, so must come from your own report. Judging from ranges we normally see, your FT4 is very bottom of range.
Sounds like you might need an increase in your thyroid med. And do ask for the Vitamin B12 test.
I know my TSH was 6.11 in January, Vitamen D was 10. My Free T4 was 0.8. At that time my doc just put me on 50,000 units of Viramin d a week for 2 months. My last check up my TSH was even higher I can't remember the value and my T4 was still 0.8 so she started me on 50mcgs of levothyroxine. My vitamin d is now at 31. I don't think I have had my B12 checked.
Having been low in Vitamin B12 and D, I have to agree that B12 wins the contest, when it comes to debilitating fatigue - mine was even worse than hypo fatigue. You should get your levels tested.
That said, it takes at least 4-6 weeks for the levo to reach full potential in your body, but that doesn't mean that you will feel better right away. It can take quite some time before symptoms may all go away. Many people still need med adjustment, as time goes on.
Please post your lab results, along with reference ranges, so members can better assess your actual status.
Iron, vitamin B12 and vitamin D are common deficiencies found with hypothyroidism. All three are causes of fatigue. Depending on how low you are to the how severe the fatigue is. Having had a severe deficiency of all three, vitamin B12 wins the contest in the fatigue stakes hands down.