Final answer:
The priority nursing intervention is to administer an epinephrine injection.
Step-by-step explanation:
The priority nursing intervention in caring for a client experiencing an anaphylactic reaction is to administer an epinephrine injection. Epinephrine helps to relieve the symptoms of anaphylaxis by increasing blood pressure, relaxing bronchial smooth muscles, and reducing swelling that can block the airways. It is a life-saving treatment that should be given as soon as possible to prevent further complications.