Cats can suffer from allergies too. Often they are allergic to the same things we have allergies to.
Airborne particles like pollen or dust can irritate nasal passages and lungs. They can have allergies to certain foods, drugs like antibiotics, anesthesia, household cleaners and deodorants. As with dogs, the most common allergy is to fleas.
If your cat scratches excessively, has diarrhea or vomiting, hair loss, inflamed ears, skin eruptions, it could indicate an allergic reaction.
Your vet can test your cat to deterimine what the allergy is. Then it can be treated, with antibiotics if an infection is present or antihistamines and/or prednisone.