T3 tests are often useful to diagnose hyperthyroidism or to determine the severity of the hyperthyroidism. Patients who are hyperthyroid will have an elevated T3 level. In some individuals with a low TSH, only the T3 is elevated and the FT4 or FTI is normal. T3 testing rarely is helpful in the hypothyroid patient, since it is the last test to become abnormal. Patients can be severely hypothyroid with a high TSH and low FT4 or FTI, but have a normal T3.
https://www.thyroid.org/thyroid-function-tests/
你先生可以按醫囑嚴格按時按量服用levothyroxine, 觀察效果：如果症狀真好轉很多，應該是個好消息啊。最好是症狀完全解除了，雖然我覺得此時也難說。有時藥物顯示有效是可以幫助做診斷的。你真不容易，抱抱。
還有這個網站能提供不少有關各類化驗的信息：
https://labtestsonline.org/tests/free-t3-and-total-t3
