Am I allergic to cats? Please help!?

I have had cats all my life, but only 1 at a time. I'm 15, and I have 3 cats and 2 dogs. I like dogs, but I'm always around my cats, holding them and petting them. However, I have had really bad allergies ever since around October, and it is now May. I sneeze a lot (once I sneezed 13 times straight) and my nose is always stopped up or runny, and I have to breathe with my mouth when I sleep because I won't be able to breathe either any of my nostrils. My eyes are also sort of itchy, and I rub them a lot. About two weeks ago, I woke up and rubbed my eye, and when I looked in the mirror my eye was bloodshot red. It went away about 4 hours later, but sometimes still I will rub my eye and it will be a bit red. Could it be from my cats? Because I think having allergies for this long is a bit ridiculous. And is there anything I can do about it? Will I have to get rid of my cats? Because there is no way I could do that. They're like my children hahaha I love them so much. Thanks in advance!