If seen in the ER, and released, can the staff that treated the patient ask the nurse coming on duty questions about the patient?
Doctors and patients have privileged communications, which means that patients can share sensitive information with their doctor with the expectation that the information will be kept private. Typically, however, the doctor must be able to share such information with his/her staff and nurses, with those people also being bound by the confidentiality requirements.
There are federal laws governing privacy of health information: The Health Insurance Portability and Accountability Act (HIPAA). You might refer to the link below for more information. Additionally, your state might also have rules and regulations in place which may address your question.