YANBU. My DD started secondary with a broken collarbone. A consultant orthopaedic surgeon advised no PE until half term - unprotected break because you cant put a collar bone in a sling.
I set all this out in a letter addressed to the head, as advised by the office. After three weeks the PE teacher ordered my DD to bring kit and get changed. She couldn't use a ruck sack, she couldn't carry two bags. She asked me not to call school because the teacher was so scary. As the adult I spoke to the head of KS 3, as advised in the event of problems or misunderstandings, explaining that dd hadn't wanted me to get in touch but I was concerned about her taking two bags, refereeing/registering where a ball could whack into her healing break. Told not a prob, it would be sorted.
The next PE,lesson the cow bawled her out and tod her next time to complain to her and not her mother.
I made a formal complaint and the head took it seriously; the head of KS3 was horrified. That it happened at all, spoke volumes about the school's mgt though.
Infected toe needing sock and shoe changing (into borrowed ones must contravene Elf and Safety.
I'd write a polite letter to the head and request clarification about the procedure to be followed. If it doesn't stipulate a fit note with adjustments specified, they should have accepted your note. Ask them to confirm why they did not and that they confirm too that the lent socks and trainers have been permanently disposed of.
These people actually wouldn't get away with it in the real world where they have to manage adults. Most organisations have policies around dignity and respect. I shouted at dd's ht once she told me not to (another H&S breach and far more serious) and I merely said I was mirroring how her office staff had just spoken to a succession of girls. Admittedly the school had just breached a setios safeguarding issue and we had already decided to move our dd the following term.
The head's departure was announced before dd left. There were worse things going on.
Not all teachers are beyond reproach and not all young people are insubordinate liars.