How do I write an excuse letter for my p.e. teacher?(read description!)?

Okay,so I went to the doctor because I was feeling sick and had a bad cough.The doctor gave me a doctor's note to not do anything in p.e.I showed my p.e. teacher and she didn't believe it was a real note,but she believed this other girl with another sickness note.And she still made me do exorcises and now I feel worse.(And,she gave me a zero for the day,but not to the other girl)How do my parents write a parent note to let her know that she can't make me do anything because my cough will get higher?