The high TgAb indicates Hashimoto's. Have you had thyroid tests, other than TSH done? You should also have had Free T4 and Free T3, which are the actual thyroid hormones, while TSH is a pituitary hormone and only an indicator of thyroid status. If you've had Free T4 and Free T3 tests performed, please post the results and their corresponding reference ranges, so we can see your actual thyroid status.
Most important, do you have symptoms of a thyroid condition? If so, what symptoms do you have?
Are those Free T4 and Free T3 or are they Total T4 and Total T3? I'm sure you have it right, but can you please recheck the T3 result and reference range? That looks more like what we, typically, see as a Free T4 result and range than Free T3.
What prompted the tests to be done, if you have no symptoms? They, typically, are done as the result of symptoms.
Many people don't have symptoms in early stages of Hashimoto's if you have it, as there hasn't been enough damage to the thyroid to affect its production of hormones.
Tests for Total T3 and Total T4 aren't very helpful, as they're somewhat obsolete, but the Free T4 done a few months ago is helpful. That's at 93% of its range, which quite high. Was there a TSH done with the Free T4 when you had the headache a few months ago? If so, what was it? Was there any diagnosis made?
Do you think you could get both Free T4 and Free T3 repeated? It's possible the high Free T4 was a "spurt" before your thyroid production declined, as sometimes happens with Hashimoto's.
Hair loss is, often, a thyroid symptom. Have you looked any lists of possible thyroid symptoms to make sure you don't have any other symptoms?