Dogs can be allergic to anything we can be allergic to — presumably even to us!
Fortunately — and despite what your dog might tell you — dog allergies to cats are very rare.
And all that That itching and scratching when he’s around the cat? He’s nervous or stressed. (Maybe because he hasn’t been very nice to the cat and is worried that the cat will seek revenge.)
Many dogs are allergic to certain foods or certain plants, however.