Being a mom and teacher, I would go to your nurse, and ask them to write something in your behalf. I'd also inform your parents/guardian and school counselor, because I think it's inappropriate for the teacher to make YOU write a note. If he insists, just write
Dear Teacher,
I am currently unable to participate in swimming, as I'm having my monthly cycle.
You'd think he'd want more verification, maybe from an adult!
Sigh...good luck!