Final answer:
The nurse should urgently apply oxygen to address the patient's potential hypoxemia and immediately notify the healthcare provider due to the concern for a critical condition such as pulmonary embolism.
Step-by-step explanation:
The priority nursing action for an older adult patient who reports shortness of breath, slight chest pain, and a feeling that "something is wrong", with vital signs including a respiratory rate of 36 breaths/min and an oxygen saturation of 91% on room air, after a left total knee arthroplasty should be to apply oxygen immediately to manage potential hypoxemia and then notify the healthcare provider without delay. The symptoms described are concerning for a pulmonary embolism (PE), which is a critical and life-threatening condition that requires urgent attention. Administering pain medication without addressing the potential respiratory issue could exacerbate the patient's condition.