Before discussing the tests, please tell us about all the symptoms you have, since those are even more important than biochemical tests. Also if tested for Vitamin D, B12 and ferritin please post those as well.
First thing is that T3 Uptake, Total T4, Free T4 Index, and Total T3 are outdated and not very useful. So don't waste your money there. The most important indicator of thyroid status is the presence of symptoms that occur more frequently with hypothyroidism. Next are Free T4, Free T3, and RT3, (although RT3 dominance is a low frequency problem, it is useful to have a baseline test). Even though most doctors have the "Immaculate TSH Belief", it is affected by so many things that at best it is an indicator only at extreme levels. Your Thyroglobulin result indicates primary hypothyroidism (Hashi's) even though your TSH is well within its range.
Another important thing to understand is that hypothyroidism is commonly assumed to be due to low thyroid hormone levels. In reality there is much more to it than that. Hypothyroidism should be defined as "insufficient T3 effect in tissue throughout the body due to inadequate levels of, or response to, thyroid hormone". So there is much more to hypothyroidism than just the usual TSH test and sometimes a Free T4 test. So there is no biochemical test that can be used as a pass/fail decision about a person's thyroid status. The best way to evaluate a patient for potential hypothyroidism is an integrated approach, with a full medical history, evaluation for symptoms that occur more frequently with hypothyroidism, and expanded biochemical testing to include Free T4, Free T3, TSH, TPO ab and TG ab (usually only if TSH is high and TPO ab is negative). Cortisol, Vitamin D, B12 and ferritin should also be tested.
From your symptoms and your FT4, FT3, RT3, TSH and TG ab results it appears likely that you are in the early stages of Hashimoto's Thyroiditis. Note your FT4 result of 1.1 and FT3 of 3.2, compared to these words from an excellent thyroid doctor. "The free T3 is not as helpful in untreated persons as the free T4 because in the light of a rather low FT4 the body will convert more T4 to T3 to maintain thyroid effect as well as is possible. So the person with a rather low FT4 and high-in-range FT3 may still be hypothyroid. However, if the FT4 is below 1.3 and the FT3 is also rather low, say below 3.4 (range 2 to 4.4 at LabCorp) then its likely that hypothyroidism is the cause of a person's symptoms." I'd say your test results fit this description.
Since there are no pass/fail tests for hypothyroidism that have adequate sensitivity and specificity, every tentative diagnosis is basically a probability theory that must be tested with a therapeutic trial of thyroid medication that adequately raises FT4 and FT3 levels. If symptoms improve, the theory is confirmed and the levels should also then be optimized for max effect. I think the best way to describe it is that the doctor should prescribe thyroid medication as needed to eliminate signs/symptoms of hypothyroidism, without creating signs/symptoms of hyperthyroidism. That intermediate state is called euthyroidism and that is the goal.
In addition to optimizing FT4 and FT3, there are other important considerations as well. First is cortisol. Low or high cortisol can cause adverse effects for a patient taking thyroid med, so it is recommended that cortisol should be tested and confirmed as adequate before starting on thyroid med. In addition Vitamin D, B12 and ferritin are very important so those should be tested and supplemented as needed to optimize. D should be at least 50 ng/mL. B12 in the upper end of its range,a nd ferritin should be at least 100.
Now, most important of all is that you need a good thyroid doctor, which are in great demand and short supply. That does not necessarily mean an Endo. Unless you have direct feedback from other thyroid patients the odds are not good for finding a good thyroid doctor , so, if you are interested, I have several sources for Chicago area doctors that have been recommended by other thyroid patients.
If you want to confirm what I have said, I highly recommend reading at least the first two pages of the following link, and more if you want to get into the discussion and scientific evidence for all that is recommended.
Forgot the link.
I just sent a PM with info. to access, just click on your name and then from your personal page click on messages.