In English, a sick cat is called a "sick cat". The phrase comes from the fact that the word "sick" in English can be used to describe an animal that is not feeling well. Here are some example sentences with the Chinese translations:

The cat is sick, so we need to take it to the vet. (猫生病了，所以我们需要带它去看兽医。)

I think my sick cat needs some medicine. (我想我的生病的猫需要吃药。)

The sick cat was lying on the couch, looking very weak. (这只生病的猫躺在沙发上，看起来很弱。)