What pressure did the teacher use? I’d simply say ‘my kid gets regular pediatric appointments and beyond immunization records I choose not to share anything’. I have not (yet) been in your situation
I did tell her something along those lines and his pediatrician did not agree with her. She continued to make comments on his work and sometimes even to him - that he could be doing so much better with meds. I complained to the principal about this, but didn’t really pursue it because I’d already made my mind to homeschool at that point. He was crying every day over school.