Is it possible to be allergic to one cat and not another?

I have three cats. Tabby and Timmy don’t bother me at all, but if Tony sits on my lap or rubs on my arm or neck I turn bright red, get hives and itch insanely for a while. I’m assuming I’m allergic to his dander, but I’ve never heard of a skin allergy to a cat, and just the one and not the other two? Does anyone know anything about this?