Oh yes - they can have allergies just like we do and even catch colds.
My mom had a Pekingese that was allergic to grass - her belly would get red and she'd itch. I think we had a hydrocortisone cream for that...
When I worked as a vet tech I remember explaining to an owner how to figure out the dosage of benedryl that a cat needed because he had seasonal allergies. The lady said: "Well, won't that make him drowsy?" And I came back with: "He won't be operating heavy machinery right? Besides, don't they sleep 19 hours a day anyhow?"
