Looking at your labs, nothing is abnormal. You are WNR (within normal range) for all tests shown. Hashimoto's is a possibility, you'll likely have to discuss your thyroid and Hashimoto's in depth with your physician. To be on the safe side I would get a referral for a Rheumatologist, just in the off chance you have an auto-immune issue that's not being detected. You have no ANA reults or ANA titer, you should have those two blood tests run and see a Rheumatologist.
In spite of what many doctors will tell you, TSH is a pituitary hormone that is totally inadequate as a diagnostic for thyroid issues. At best it is only an indicator to be considered along with more important indicators such as symptoms and also levels of the biologically active thyroid hormones, Free t3 and free T4. Of these Free T3 is the most important test because it largely regulates metabolism and many other body functions. Scientific studies have shown that Free T3 correlated best with hypo symptoms, while Free T4 and TSH did not correlate at all. Alsom be aware that even though TSH is only a fair indicator, over 10 years ago, the AACE recommended that the range should be reduced to .3 - 3.0.
So, you have hypo symptoms, and your Free T4 is too low in the range. You also haven't even been tested for Free T3. I would expect that you will find that, at best, Free T3 is also low in the range, if not below.
I suggest that you should go back and request to be tested for Free T3 and Free T4. If the doctor resists, just insist on it and don't take no for an answer. Also, since Hashimoto's Thyroiditis is the most common cause for diagnosed hypothyroidism, you should request to be tested for the thyroid antibodies associated with Hashi's. Those are TPO ab and TG ab. Since hypo patients are also frequently low in other areas, I would also test for Vitamin D, B12 and ferritin.
Assuming success in getting those tests done, when results are available, please get a copy of the lab report and post results and reference ranges shown on the lab report and members will be glad to help interpret and advise further.
Sorry my post cut off the values.
Test Name Result Reference Range
FREE T4 (THYROXINE) 0.76 0.73-1.95 NG/DL
TSH 3.1 0.5-4.7 UIU/ML
TESTOSTERONE 45 17-76 NG/DL
SEX HORM GLOBULIN 134 23-152 NMOL/L
FREE TESTOSTERONE 0.3 0.3-1.5 NG/DL
ESTRADIOL <12 46 - 143 PG/ML