Do you by any Chance have scented candles, air wick fresheners, incense, in the house. Do you use products like febreeze? Cats sense of smell is extremely acute. Strong fragrances can make them very sick. Essential oils can be deadly to felines. Make sure you use an unscented litter. Remove all fragrances from the home, and be careful will all cleaning products that have a strong odor like pine sol, Lysol. Cats fine prey like mice by smelling their location in the dark. The olfactory senses can go berserk when they encounter strong odors. This would be the first place I would start. Also bear in mind that after so many rounds of anti-biotics and immune suppressing Prednisone that the cats natural immune system has been disabled. The good bacteria should be replaced in order to help the natural balance to return.