Your TSH actually looks good; my doctors would love it if mine TSH was anywhere near yours... lol What's the reference range for the Free T4? Ranges vary from lab to lab and have to come from your own report for the best comparison...
Unfortunately, they didn't test Free T3, which is the hormone that's used by individual cells in the body, whereas Free T4 is a "prohormone" or storage hormone. It must be converted to Free T3 prior to use. Sometimes, there's a malfunction in the conversion process or a malfunction in how the body uses thyroid hormones, so further tests would be in order.
Your TPOab is negative, which indicates that you don't have Hashimoto's, but there's another antibody test that you need to get to absolutely rule it out - well, even that won't completely rule it out, but you need it anyway. That's Thyroglobulin Antibodies (TgAb); both TPOab and TgAb are markers for Hashimoto's and need to be tested. Some people have been diagnosed with negative antibodies, based on characteristics of ultrasound, so you should ask for that as well.
Because of the fatigue/exhaustion, I'd suggest that you ask for a vitamin B-12 test. Vitamin B-12 is necessary for energy production and deficiency can cause horrible fatigue.
You should also ask for Vitamin D and ferritin tests as a deficiency in Vitamin D can also cause fatigue/tiredness... Ferritin is the iron storage hormone and iron is also necessary for energy production and red blood cell production. Red blood cells carry oxygen to cells throughout the body and lack of oxygen causes tiredness and can cause lightheadedness... Vitamin B-12 also has a part in red blood cell production.
Cortisol tests might also be advantageous because too much/too little cortisol can also cause exhaustion.
I had my TSH tested for decades and it never changed - always 1.4 to 1.6. The moment Hashimoto's thyroiditis showed up my TSH went up to the 2's (both thyroid antibodies high) then next lab back to the mid 1's then back up again. By the mid 3's I gained weight. By 6 I was on thyroxine (should of started 4 years before but could not find a doctor to prescribe thyroxine grrr). I was tested for celiac as it is linked with Hashimoto's thyroiditis but thankfully do not have this (I like pizza lol).