Wow, and endo who actually takes symptoms into account, that's rare.
Labs usually take about a week or less to get back. You may have to call the Dr's office to ask for a copy of your results.
Any chance they also did a TPO (thyroperoxidase) antibody too? It's a more common marker for Hashi's than the TG (thyrogolobulin) that you've had done. Also the total T3 and total T4 he did won't be much use but it's good he's doing both free T3 and free T4. At some point I'd request ferritin, vitamin B12 and D levels too.
Cortisol testing will tell if your adrenals are functioning well. Unfortunately a serum cortisol is just a snapshot and doesn't tell if you've got adrenal fatigue unless the blood draw catches the fluctuating cortisol level in your body at the low or high point. Diurnal saliva cortisol testing is more effective and sensitive for this.
Secondary hypothryroidism is when your thyroid is not producing enough hormones due to a problem in the feedback loop, usually from pituitary dysfunction (as opposed to the thyroid itself malfunctioning, which is far more common). Low TSH coupled with low FT3 and FT4 levels is a good reason to look for secondary causes for your hypothyroidism.