Yes, you are entitled to medical care in jail. You may have a personal injury claim against the jail/State of North Carolina. This will depend on if you had any long-term damage, and other facts of your case. Please feel free to contact our office at 919-783-5900 to discuss further.
In most cases, this is not an issue of state law, but of your rights under federal law. Call a personal injury lawyer who specializes in this area of law.
I have added a civil rights tag to your question. Generally speaking this is more of a civil rights question. You would be best served by having a civil rights attorney answering this. But, generally you are entitled to medical care, even if incarcerated.