With the thyroid, your GP won't be able to do a full thyroid panel. The lab won't let them, if they are an NHS GP. All they will do is TSH and (if you're lucky) T4 and that's no way near a full thyroid panel.
The best full thyroid panel around is the Blue Horizons Platinum test which covers TSH, free T4, total T4, free T3, thyroid antibodies AND reverse T3/rT3. It also includes cortisol and ferritin and a few other things. It's not cheap, about £140, but it's the only test in the UK which you can order yourself and which includes rT3. It needs a venous draw due to the rT3, so you have to take the pack to someone to draw your blood. Usually aesthetics clinics offer this service if they are run by nurses, that's where I go. It's £30 for a blood draw.
Then if you need thyroid meds, I recommend Dr Momi and Functional Thyroid Health (google for website). He accepts any test results including Blue Horizons and will prescribe whatever combo of T4 or T3 you need and he doesn't go by TSH and you can see him on Zoom.
However, again, he is 'only thyroid'. So when it looked like my stuff might be pituitary and go beyond thyroid, he couldn't help there.
I've also spent thousands I don't have