Final answer:
The client with chest pain and shortness of breath should be treated first due to the potential seriousness of their condition.
Step-by-step explanation:
The nurse working in the emergency department should recommend the client with chest pain and shortness of breath for treatment first. This patient presents symptoms that could be indicative of a life-threatening condition such as a myocardial infarction (heart attack) or pulmonary embolism, both of which require immediate medical attention. In contrast, the clients with a sprained ankle, minor burn on the arm, and a rash with itching are likely to be experiencing less serious conditions that don't need immediate intervention.