Itchy skin, sores, and the fat lip
(likely an eosinophilic granuloma) are indeed all allergy related. The fat lip
also is commonly secondarily infected with bacteria, so I would recommend a 2-3 week course of antibiotics if not already done. The three types of allergies are parasite (fleas, mites), food allergy, and pollen/dust allergies. If your cat is already on a good flea control such as Advantage or Revolution, then parasites are less likely.