In view of the history of allergy
given by you, most likely your symptoms are as a result of allergy to cat. Cheese is also known to cause allergy in people who have allergic diathesis. My suggestion is you should avoid handling the cat-let some other family member do it. If you cannot avoid it, take an antihistaminic, a monteleukast and inhalers like aerocort. Avoid cheese also as much as possible or at least till your symptoms subside.