I agree with both flyingfool and Red_Star; TSH is definitely not enough to base a diagnosis on.
If you can get your doctor to test the Free T3 and Free T4, suggested by flyingfool, do so. I'd also recommend that you get tested for thyroid antibodies, Thyroid Peroxidase Antibodies (TPOab) and Thyroglobulin Antibodies (TGab). These antibody tests will determine whether or not you have Hashimoto's Thyroiditis, which is an autoimmune disease that destroys the thyroid over time. Hypothyroidism is the end result.
It's entirely possible to be in the early stages of Hashi's, have hypo symptoms and still have so-called "normal" TSH.
If you can't get your current doctor to do these tests, you should find another asap, or you will be kept very sick.
My mother's current thyroid tests show a TSH of 2.5mU/L, free T3 and free T4 in the upper optimal range. She does eat brazil nuts (full of selenium) which has lowered her TSH and thyroid antibodies to some degree but symptoms persist. She has various hypothyroid symptoms including the classic low body temperature and a third of her eyebrows missing (a symptom she has had for many years) which is a late sign of hypothyroidism called the queen anne sign or sign of hertoghe.
Her FNA biopsy (for large thyroid nodules) showed a goiter and Hashimoto's thyroiditis. But no doctor will treat her as she has normal TSH. So she had decided to try my T4 medication. The fluid in her fingers improved already. Wish mine did lol! But the point is going by a single TSH test can very easily miss a diagnosis of thyroid disease.
Well TSH testing is not enough testing to determine that you are not sufficient for Thyroid.
you MUST be tested for at least the Free T3 and Free T4. And understand that many people need to be well up into the "normal" range in order to feel well with these 2 hormones. In fact many people report that they need to be in the MIDDLE of the range for the Free T4 (FT4) AND (that means in addition to) They need to have their Free T3 (FT3) in the UPPER 1/3 of the range. This is a rule of thumb but seems to provide a much more accurate reflection of wellness than the far too broad reference ranges most labs use.
If the Dr refuses, the advice generally is to find another Dr who will test for these.
Make sure you ask for the FREE hormones. Otherwise you'll likely get tested for "total" T4 and Total T3. The total test is outdated and of little value. This is because it counts BOTH usable and useless hormone molecules. Once a hormone becomes attached to a protein molecule it becomes useless. Yet the "Total" test count these useless molecules along with the usable ones which are "free" from being attached to a protein.
The "total" test is analogous to checking how much fuel gets to the engine by checking the fuel level in the gas tank. You really need to check what is reaching the engine. This would be the "free" T3 and FREE T4 tests for Thyroid which only counts the usable hormone. Which is really what you want.