MG has made some excellent points in her post and congratulations MG on becoming a mum again
I'm no expert so can only say what my own doctor has been doing for me. I only began meds in May 2008. I've been a very difficult case for my doctor. He began by retesting me every 6 weeks and that's what we're still doing. I've had some set backs due to a couple of stressful situations along the way and each time it's set all my figures into turmoil. I've realised that stress, even minor ongoing stress, worry, anxiety, has a very bad effect on my health, more than i'd ever realised before. So i'd say stress is my biggest trigger and likely has been all along.
My antibodies are very high so they get tested every 6 weeks for now and he also rechecks my TSH, FT4, FT3, Cortisol, Ferritin, Vitamin D and sometimes does the Reverse T3 and i think ACTH. These tests are done as a blood test each time.
As my estrogen is in excess, he also retests that a few times per year to see whether we are getting it under control or not. Twice a year he'll recheck my iodine absorption rate as i'm supplementing iodine too. Once a year he'll get me to do a stool analysis test to check for my absorption and digestion of certain things as he discovered my pancreas wasn't producing sufficient enzymes to digest protein foods. He's done a liver detox test once to see how that is working due to poor liver detox being a contributing factor to excess estrogen being stored in the body. Twice now i've done the saliva cortisol test to see how my cortisol levels decline throughout the day (samples from 6am,12noon, 6pm,10pm). I've also done twice a total hormone saliva panel test to check ALL hormones as my testosterone was high too plus low progesterone, but now that my thyroid hormones and cortisol are better the testosterone has self corrected.
I think that's it for the tests i do regularly or have done. Not all doctors will do that though, but my doctor has Hashimoto's himself and he's involved in studies into Hashimoto's too, which is a good thing for me, but still i wasn't prepared for how long it takes to correct everything which was affected by Hashimoto's and all the testing involved.
My tip would be, definitely keep tabs on your full thyroid panel, plus your ferritin, Vitamin D, B12 and your cortisol levels.