I am suffering from something similar with my new kitten (he's 5 mo.). He was an outside cat the first 4 mo. or so of his life. This year here in central Tx. the pollen and other allergens have been horrendous. A friend on here helped me with understanding this. The cat licks his fur..then carries the allergen in his mouth and licks his fur again. Mine even scratches me on the hands and I think, transfers the residue from his claws to me producing little red itchy whelps on my hands. I have to wash my hands every time I touch that cat.
My husband hit 40 and got allergies to grass, horses, cats and tree pollen. He had never had allergies before. The allergist told him it's pretty common for one's reactions to things like that to change in the course of one's life.