It could be an allergy to something on board Ryanair planes? I realise the materials are pretty standard across the board, but there could be one small thing that sets this off? A material used that differs to other carriers? Crew Uniforms? Something for sale on board? Like someone else suggested, is it always on a certain route? Perhaps there is something in the airport at either end? Is there something you do differently when you fly Ryanair? For example, do you take a different carry on bag or buy food to take on board from somewhere?
I have flown Ryanair dozens of times (last flight was a few days ago), some long and some short sectors and can't say I've noticed feeling any different to flying with any other carrier.