cat or seasonal allergy

so my husband's cat has joined us since about last Nov. never been a cat person but I really grew to love him. my chihuahua and him are so funny together. I never noticed anything until recently. my skin/scalp feels randomly itchy in different spots. nose feels weird. I started sneezing (not always when I'm home tho). a few months back I had one eye that waters alot (doctor said it was dry eye. we were sleeping with a,fan plus space heater). my nose drips alot (I believe I've had this a while tho. I've never had allergies. could this be seasonal or pet allergies? I went months with no problems from the cat until now.