It's very rare for humans to be allergic to other humans but yes it's possible for some people to be allergic to other people.
There was a story on a news website where a woman was actually allergic to her partner and I believe it was an allergic reaction to the partners skin but I can't remember exactly.
So although it's possible for humans to be allergic to other humans it's not very common.
Also cats, dogs and other animals can actually be allergic to humans so your cat or dog could be having an allergic reaction and the cat or dogs allergic reaction could actually be caused by you or someone in your house.