How can I get rid of a cat.....?

Alright, so I'm 16 years old and I live in a 2 bedroom condo with my mother. She's cat crazy (beyond anyone you've probably ever met) and has 4 cats. Legally, according to the condo rules, you can only have 2. Despite the fact that this is illegal, it bothers me for many other reasons. 3 of the cats are sick (uncontrollable peeing, bleeding, throwing up, etc) and I'm getting physically sick from living around them. I really need a solution to this problem. How can I get rid of one of the cats? Don't post any rude comments, I'm not anti-animal, I'm just in desperation and need to find something I can do. Animal shelter?