Hi OP, if you have funds or insurance it really helps to see specialist endocrinologists for thyroid weirdness.
At a previous address I got an NHS endocrine referral as mine has been bizarre and it was absolutely incredible to talk to someone so expert.
Unfortunately at my current address the GPs agree it's baffling and refer, the hospital team just write back saying "manage via GP, referral declined" and it goes on and on...
In a nutshell what I've experienced (with Hashimoto's, most likely triggered during pregnancy) is TSH levels from 40 (!!!) to 0.00000003.
I feel consistently exhausted, can sleep all day sometimes, and also occasionally lose consciousness and keel over... even when the tests are showing basically non-existent TSH, consistent with wildly overactive thyroid.
The endocrinologist explained that my damaged thyroid gland is super-susceptible to viruses and pathogens so will every so often be "triggered" into a frenzy - which the blood tests interpret as hyperthyroidism - while my baseline levels are still hypo.
I wonder if perhaps there's something similar going on with you? This is where speaking to an expert could really shed some light..
In all of this the main thing is how you're feeling. If I were feeling jittery and hyper then I'd trust myself and stop taking the extra meds.
Are you TTC at the moment? If you are then that's a good reason for them to bump your referral as abnormal TSH levels are a strong indicator for pregnancy loss and birth defects... Extra important to get it sorted properly if that's the case.
Wish you all the best with it.