The cat in dreams could have many different explanations, depending on the circumstances of the dream. The cat that is dreamed of you and is being your own cat could simply be a reflection of your actual cat. The animal spends much of the time in your life, therefore it is very normal to dream about it. If you do not own the cat, but still dream of one, it could mean that you are surrounded by very mysterious people in your waking life. You should be aware of that and do not trust them, because they will always have various secrets. The cat could also denote to your personality as being very independent and a little bit arrogant person. If the cat is sick, your problems will go away very soon. No serious danger.
Read more about dreaming of Cat in other dream meanings interpretations.