Do you burn candles? I have a friend whose cat did this and the vet said allergies but no clue as to what she was allergic to. Finally after process of elimination she realized it was the perfumes from the candles she burned. She stopped burning candles and the allergies went away. Granted it's been about 8 years now and she misses candles!
It was worth it to her though!
Good Luck to you and your poor baby!