Besides the cat possibly faking an allergy to the dog in the hopes you get rid of Fido, can cats really be allergic to dogs? Can dogs be allergic to cats? Can our pets be allergic to us?

"The answer to all of these is yes," Raelynn Farnsworth, of Washington State University's College of Veterinary Medicine, told National Geographic."It's rare, but dogs can be allergic to cat dander and people dander and vice versa. For everything."

Dander is made of tiny cells that our pets - and humans - shed from hair, fur or feathers. Pet allergies also include allergies to flea saliva and some foods.

The most common clinical signs for dogs are skin inflammation, itching, sneezing and runny noses, Farnsworth told National Geographic. Cats' symptoms show up as miliary dermatitis, resulting in little scabs or missing hair, usually around the head and neck area.

Pets can be tested for environmental allergens, whether the issue is seasonal or year-round, Christine Cain, of the University of Pennsylvania School of Veterinary Medicine, told National Geographic. "We routinely test dogs for reactions to cat dander," Cain said. "This includes a small amount of allergen placed under the skin to test for reactions, just like in human allergy testing."

But, what if the allergen is you?

"It always makes owners kind of sad if their reaction is to human dander," Cain told National Geographic. But don't despair. You and Fluffy don't have to part ways. "If we have a patient that reacts to human dander, usually they react to other allergens as well," Cain said. Your pet can get allergy shots, like a human would (or oral drops) that contain small amounts of the allergy culprit. Over time, your pet's system will learn to ignore the allergy.

Sorry, Fluffy. Fido stays.