Happens. All cats produce allergens but some may produce more or less allergen that others. In general males make more allergen than females and neutered animals make less allergen, in general.
Alskinlessl breeds. The allergens (the materials that you are allergic to) are present in nearly all breeds. Some cats produce more of the allergen than others. The material is in saliva and in the skin.
Possible. Recommend allergy testing by a board certified allergist.