For reasons too lengthy to get into, the reference ranges are so broad that being "normal" frequently is inadequate to alleviate symptoms. And never forget that symptoms should be all important. My definition of a good thyroid doctor is one that will treat your symptoms by testing and adjusting the biologically active thyroid hormone (FT3 and FT4) levels with whatever type of medication is required to alleviate symptoms, without being constrained by resultant TSH levels.
I suggest that you tell your doctor that this is the approach you would like to take and start with testing for FT3, in addition to the FT4 and TSH testing. You may also need to be tested for thyroid antibodies, by testing TPO ab and TG ab. If your TSH continues to run low, along with low elevels of FT3 and FT4, then you may need your pituitary function tested. Since hypothyroidism frequently has side effects, you should also test for Vitamin D and B12 levels.
Along with testing B12 and Vitamin D levels, also have your ferritin level checked. Ferritin is a protein that stores iron for future use. Symptoms of a low ferritin count overlap with symptoms of hypothyroidism, B12 deficiency, and Vitamin D deficiency.
Make sure that you ask specifically for the ferritin test. A CBC (Complete Blood Count) does not include ferritin. You can have a very low ferritin count and still have normal hemoglobin and hematocrit counts (both checked via the CBC).