Final answer:
The nurse's first priority is to stop the PRBC infusion immediately due to potential allergic or transfusion reactions, then assess vital signs and notify the physician for further medical intervention.
Step-by-step explanation:
When a patient reports symptoms such as itching and swelling in the hands and arms thirty minutes after starting a packed red blood cells (PRBC) infusion, the first priority for the nurse is to stop the infusion immediately. This is because these signs may indicate an allergic reaction or a transfusion reaction, both of which can potentially be life-threatening if not addressed promptly. Subsequently, the nurse should assess the patient's vital signs, notify the physician, and prepare for further medical intervention as per the facility's protocol for managing transfusion reactions.