After you touch the cat and find the eyes itchy, you may get the eyes infection through the cat's contagious bacterium. You should use the eyes drops with anti-inflammation to make the eyes feel comfortable. Then you could use the warm compress to make the eyes feel comfortable. You'd better get the bacterium out of the eyes. You should better not touch the animals next time.
Maybe you're the type of person who is allergic to the fur of cat. People's eyes and skin are very easy to get itchy after touching a cat when they are allergic to cat's fur.
You'd better not touch cat anymore, because they may cause more serious problems, such as inflammations. Now, you need to clean your hands at first, then clean your eyes with pure water or physiological saline.
Well, looks like there is something bad happened to you, because I suspect that you are allergic to some small pets such as cats or dogs, for there are lots of bacterium on their bodies, so it would not be strange for you to have itchy feelings. For this moment, you need to get some medicines from the hospital, then try to avoid those allergic sources and take care of your eyes and health.