Whom can I sue if a nurse gave me the wrong medication?

You can sue the individual nurse if their medication error fell below the standard of care that a competent nurse would have met. In addition, you may be able to sue the hospital that employs the nurse. You would need to show that the nurse was acting in the scope of the employment relationship and that they were not supervised by an independent doctor (a doctor who was not a hospital employee). If they were supervised by a doctor who was a hospital employee, you still may be able to sue the hospital.