Why is my air conditioner periodically blowing warm air?

It's only a little over a year old, it's a General Electric model with 5,200 btus. Today, I took the whole front grill off and vacuumed the coils. They were very wet, and there was like a thick layer of wet cat hair stuck to the the coils. After I got it all off, it seemed like it was working better but it just started blowing warm air again. I don't want to take it to a shop, because it was like $99 new, I'm just wondering if maybe I'm overlooking something or if someone could tell me a brief idea of what may be wrong with it. The back coils are virtually spotless and it is slightly tilted back for optimum drainage. One thing I thought to do would be drill a little hole in the bottom of it for more drainage? I'm not sure it's due to freezing up, because it blew warm air after 15 minutes of being on yesterday. It will usually alternate between 30 minutes of beautiful, cool air and 10 minutes of warm. If it's something small, I could take it to a shop, but I wouldn't want to spend any more than what I paid for it to fix it, cause it would make more sense to just buy a new one.