well, 24 hours with my old (really old - like, probably 20 year old) flanny sheets and the rash has dramatically improved.

It's basically not on his face any more except for directly under his lip (where he had some drool rash anyway from teething) and even on his legs where it had been worst, there is now less of it, and much of what remains is now pale pink and slightly raised instead of quite red and raised.

DH may have been right! Or maybe it has just run its course, and this is a coincidence.

Either way, I'm glad it's going, and hope it's soon gone.

Might run the sheets through another extra wash, just in case ... and if the rash comes, source some new sheets!
Polyester doesn't allow the skin to breath well so it may have been some sort of heat rash/reaction to it. You would probably find your old flannel sheets are 100% cotton. I am a bit of a bed nazi for that and only allow natural fibres for bedding and pjs. It's just so much nicer on your skin.