They become oozy and smelly and they spread very quickly. Allergies are not limited to dogs, cats get them as well. Cats can develop swellings around the mouth and on the lips or chin. They can also develop small wounds that we call granulomas on the face and neck. I even see the occasional cat with waxy and irritated ears caused by their allergies.
Some cats get crusts and scabs all over.
The best way to treat any allergy is to avoid the substance that you are allergic to. That is not too difficult if you are allergic to bee stings, but I haven't figured out how to avoid breathing air and it would be a real trick to try to teach your cat or dogs not to breathe. We use steroids to treat allergies in pets. Steroids will block allergies and stop the allergic reaction. We can administer steroids as a single long acting shot, tablets given daily, or in creams and topical medications.