Remember if you still suspect thyroid there is the Reverse T3 test. My frees were a little lower than yours but when they ran the Reverse T3 it was very elevated and it should not be. That means that my thyroid is making too much of the Reverse T3 hormone and it is useless to the body and prevents the regular T3 from doing it's job so I have to take meds to compensate for that. It's a little expensive though, I think that test was $170.00 where the Free's were $60.00 each.
For a complete thyroid panel your doc should have definitely ran the antibodies, you can have good labs but antibodies elevated.