Poor you and poor teacher
Unfortunately it would appear impossible to keep gossip, rumour and pure guesswork out of the playground, and my guess is the headteacher is probably aware. I think if it was me, I would speak to the head, only saying that it appears the children are talking about the teacher and diagnosis, and that maybe they needto give further thought to what should be told. Not sure if I'm making myself very clear. Don't think you need to say which girl started it.