Can cats get allergies? Yes. Cats can definitely get allergies just as their people can.
One of the most common cat allergens is dust. So, it's important for your cat to have clean, comfortable areas where they can rest and play that are free of dust.
Other inhalants can also trigger allergic reactions in cats. These include mold which can be found in areas that are moist and warm.
Pollen is also a cat allergen. Your cat could definitely be exposed to pollen if they go outdoors especially during certain seasons.