I looked under your Countys ordinances and also Rock Hill, the answer is no.
If it is a dog.
If it is chickens, that is a different story.
BUT, you do have a local noise ordinance, if it is a dog and noise is bothering you.
It is unlawful for noise that would bother any reasonable person, and you could
remedy the noise that way.
Go down to your local city building and ask about that, they will tell you.
The laws in most States for what you are speaking to, is handled by the
city, or the county in which the person resides.
So if you live in Rock Hill, you will have to ask your local government.