Re: Went to the doc this am
If I remember you were getting your antibodies tested too this time?
Because I do believe that feeling better can affect some of your lab restuls, but around 90% of hypos are from hashimoto's, and Anti-TPO is roughly 90% accurate, so there's a good chance you could still be diagnosed from that since antibodies won't fluctuate as much (you can't simply become "normal" within a week antibody-wise).
As for Free T3, it isn't "necessary" as most people with abnormal results should show up with TSH and FT4, but it's better to have everything tested out just in case your fall into that small percent of people who have trouble with T3 but not T4, or normal TSH with a problem somewhere else. Doctors don't seem to care for other tests when they can cover 90% of cases with 1 or 2 tests (or so they believe).
If you are getting only TSH and Free T4 (I know my current doctor won't do anything else :/ ) and had to ask for one single test, I'd say get your Anti-TPO done. Also, if your free Thyroxine comes back at the lower end of the range again, getting your Free T3 could very well reveal your problem.
Best of luck in your fight towards feeling well!