Sorry to hear you struggled with the vaccine, I also had a horrible time after one shot of AZ.
However, to correct a myth peddled by doctors, a suppressed TSH DOES NOT MEAN you are overactive, it's entirely normal to have a suppressed TSH when on thyroxine, one is only actually overactive when the T4 AND the T3 are above the top of the range.
This misconception keeps women on stingy doses of thyroxine and feeling unwell (90% of thyroid patients are women, and it typically shows up at the menopause) - this is a key health inequality issue and one area where medical sexism is alive and well.
Unless you are thyrotoxic which can ONLY be established by a full blood panel and signs and symptoms - include rapid heart rate, sweating, anxiety, tremors, fast bowels etc etc etc then the TSH is meaningless.
Also, the fear mongering about bones and suppressed TSH is not backed up by research (most thyroid research is of poor design and of low quality).
I know all this because I am deliberately TSH suppressed for thyroid cancer, my TSH is so low the machine cannot read it, however my T4 and T3 are unequivocally normal, and yet doctors endlessly want to debate this point, so much so I have a little card to carry in my purse to get them to leave me alone and if they want to argue they need to call my endo oncologist and argue it with her!
If you feel fine on your dose and are doing well, then they really need to shut up about the TSH. It's really worth educating yourself on this as they will never let it drop, and I've had to intervene with my elderly mum to get them to stop lowering her dose because of this, she now has a note on her file.