You need to find out if you have been declared essential employee , but that usually applies to the hospital or LTC setting as far as nurses being permitted on the road.
When I worked in research the nurse manager declared that nurses were permitted on the road in a state of emergency and several received tickets for being on the road (and lost the fight in court as health normal patients doing voluntary research did not meet the OEM definition of a mandated nursing patient).
Each patient should have an emergency plan in place. I do extended care HH for pediatrics, each of my patients has an emergency plan as to who can use family resources in an emergency and who requires skilled nursing in an emergency (ie. case too complex for family to care safely for patient). Plans include local shelter resources and ensure local OEM is aware of special needs, including power company notification of specialized medical equipment. There are only a select few nurses (often the trach/vent nurses) that have been declared essential employees.
When my grandmother was admitted to HH, we had to sign an emergency plan that we would provide her care in the event of a state of emergency declaration and they created a "go bag" list of supplies that we needed to take with us (nebulizer, medications, oxygen tanks, cannula, etc.) and ensured we had a bag ready just in case.
I just checked NJ OEM and your employer has to declare and register you as an "essential employee" for you to be permitted on the road in a state of emergency (BEFORE an emergency is declared). You would be issued an official ID declaring you an essential employee.
Check your employee handbook for emergency procedures.