Final answer:
The most likely diagnosis for the 67-year-old female who has an oxygen saturation of 88%, shortness of breath, and sharp chest pain after hip surgery is acute pulmonary embolism. Option 2) is correct.
Step-by-step explanation:
Given the patient's recent surgery, presenting symptoms of shortness of breath, sharp chest pain, dried blood around her mouth, facial cyanosis, and an oxygen saturation of 88%, the most likely diagnosis is acute pulmonary embolism. Post-surgical patients are at increased risk due to potential blood clot formation that can travel to the lungs causing a blockage of one or more arteries in the lungs (pulmonary embolism). This condition can be life-threatening and requires immediate medical intervention.
While the other conditions listed (spontaneous pneumothorax, acute pulmonary edema, and right-sided heart failure) can also present with similar symptoms, the recent history of surgery and the combination of symptoms such as hypoxemia and sharp chest pain strongly point toward pulmonary embolism as the cause. Spontaneous pneumothorax typically presents without the history of recent surgery, and acute pulmonary edema and right-sided heart failure often have different clinical presentations and underlying etiologies.