Is this caused by allergies to my cat?

So I have a dog and I was allergic to her but became immune over time, but recently we got a new pet its a kitten. And everytime I pick him up I become really congested, and start sneezing alot and my nose running. Not only that if im not careful a part of my eye becomes swelled up and irritated and I have to put a clothe on it. is this caused by him too?