If your vet can't diagnose the problem, then why don't you get a second opinion? If it's a seasonal thing, then antibiotics won't help (apart from stopping the sore bits becoming infected). It could be some sort of mite (my elderly dog gets these sometimes, depending on the season) or could be one of any number of skin conditions, perhaps brought on by stress (only speculating, it happens in humans, so why not in animals?). I give Elsa oil of evening primrose, which seems to help her skin. Maybe try that - it won't hurt the cat. Get some low-dose capsules from any chemist & squeeze one a day into her food. Good luck & I hope puss gets better soon. K xx