It is always best to compare results to reference ranges, since lab results and associated reference ranges can vary from lab to lab. So please post the ranges shown on the lab report for those results. Also, please list any other symptoms you have.
TSH range 0.270 - 4.200 u[IU]/mL
T4 Free range 0.55 - 1.60 ng/dL
T3 Total range 80.0 - 187.0 ng/dL
Pre-menopausal: 3.34 - 26.72 ng/mL
Post-menopausal: 2.74 - 19.64 ng/mL
You have many symptoms that can be related to hypothyroidism. It would have been better if your doctor had tested for Free T3 instead of Total T3. There is no good reason to test for Total T3, since Free T3 tests are adequately accurate nowadays, plus only the small portion of Total T3 that is not bound to plasma protein, which is called Free T3, is biologically active. Free T3 is metabolized by all the cells of your body and produces the needed energy.
In diagnosing for potential hypothyroidism, symptoms are most important, followed by levels of Free T4 and Free T3. In the words of a good 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." Note that the FT4 value he uses is for a different range than yours, but it relates to being less than 50% of range. Your FT4 is only 32% of its range and your Free T3 is 62% of its range, which indicates that your body is trying to maintain thyroid effect by converting a lot of T4 to T3.
In addition, your TSH is above range, which may indicate the possibility of an autoimmune system disorder called Hashimoto's Thyroiditis. With Hashi's the autoimmune system erroneously identifies the thyroid gland as foreign to the body and produces antibodies that attack and eventually destroy the gland. As this proceeds, output of thyroid hormone is diminished and the pituitary increases TSH output to try and stimulate enough thyroid hormone from the gland. To check for Hashi's two tests may be required, Thyroid Peroxidase antibodies and Thyroglobulin antibodies. TPO ab should be done first and if it is negative, then TG ab should also be done. Note that TSH causes no symptoms directly. TSH is only an indicator, to be considered along with more important indicators such as symptoms and also the biologically active thyroid hormones, Free T4 and Free T3.
I don't know how to anticipate what your doctor will do when reviewing the test results. Once he sees the TSH over its range, he will then look at FT4 and TT3, and may tell you that they are within the "normal' range, and that your symptoms must be due to something else. That is incorrect. A good thyroid doctor will treat a hypothyroid patient clinically by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms, without being influenced by resultant TSH levels. Symptom relief should be all important, not just test results. You can confirm what I say by reading at least the first two pages of the following link, and then read further if you want to follow the discussion and scientific evidence supporting all that is suggested in the paper.
You can also consider giving your doctor either a link to the paper or a copy of the entire paper and ask him to review and see if he will be willing to treat clinically as described above. If not then you will need to find a good thyroid doctor that will do so.
Also, since hypothyroid patients are so frequently low in Vitamin D, B12 and ferritin, those need to be tested and supplemented as needed to optimize. D should be at least 50, B12 in the upper end of its range, and ferritin should be at least 70.