For several reasons just because your test results are within range does not assure that you are not hypothyroid. In trying to assess a person's thyroid status, the most important consideration should always be symptoms, so please tell us what symptoms you have. Also, if tested for Vitamin D, B12 an ferritin please post those results also. Test results should always be compared to reference ranges shown on the lab report. So please post reference ranges.
Test results should always be compared to reference ranges. So please post the ranges shown on the lab report for the thyroid related tests plus the iron.
Since TSH is affected by so many variables, a TSH result within range does not preclude hypothyroidism. TSH is useful as a diagnostic only when it is at extreme levels. Your Free T4 of 1.36 is at 57% of its range, which is adequate. You were not tested for Free T3, but instead Total T3. Most of Total T3 is bound to protein and thus not biologically active. Only the very small portion not bound is called Free T3. Your Total T3 of 1.04 was only at 30% of its range. If your Free T3 is at a similar level within its range, that is indicative of inadequate conversion of T4 to T3 and is too low for many people.
In addition, hypothyroidism is not just "inadequate thyroid hormone", but instead it is "insufficient T3 effect in tissue throughout the body due to inadequate supply of, or response to,, thyroid hormone". So it is not just the level of FT4 and FT3, but also the response to thyroid hormone, which is affected by a number of processes and variables. Inadequate TISSUE T3 EFFECT causes hypothyroidism and its symptoms.
In trying to diagnose a person's thyroid status, the most important consideration is an evaluation for symptoms that occur more frequently with hypothyroidism than otherwise, followed by expanded testing. You have identified a few symptoms that may be associated with hypothyroidism. The additional tests you need are Free T3, Reverse T3 and cortisol ( at least initially), Vitamin D, B12 and ferritin. All of these are important to TISSUE T3 EFFECT.
A good thyroid doctor will do the symptom evaluation and the expanded testing and then if there is a tentative diagnosis of hypothyroidism, the doctor will prescribe thyroid medication and supplements as needed to relieve hypo symptoms, without being influenced by resultant TSH results. Symptom relief should be all important, not just test results, and especially not TSH results when taking thyroid med. If you want to confirm what I have said, then click on my name and then scroll down to my Journal and read at least the one page Overview of a full paper on Diagnosis and Treatment of Hypothyroidism: A Patient's Perspective.
If your doctor is unwilling to do these tests and then diagnose and treat clinically, as described, then you will need to find a doctor that will do so. If you do not know of such a doctor, then if you want perhaps we can suggest a doctor in your general area that has been recommended by other thyroid patients.