Which of the following is a sign of internal carotid artery issues after posterior pharyngeal trauma?

A facial droop can indicate an issue with the internal carotid artery after posterior pharyngeal trauma due to its close anatomical relationship with the cranial nerves, particularly those responsible for facial movements. Trauma in this region may lead to vascular injury that can compromise blood flow or cause a stroke, potentially affecting the areas of the brain that control facial muscles. This impairment results in weakness or paralysis of the facial muscles, presenting as a droop on one side of the face.

The other signs listed, such as severe headache, severe neck pain, and nausea/vomiting, may occur in various conditions following trauma but are less specific to internal carotid artery issues. For instance, severe headaches could arise from many causes, including concussion or other types of vascular injuries. Severe neck pain might indicate musculoskeletal injury, while nausea and vomiting could result from increased intracranial pressure or other unrelated trauma symptoms. Thus, while these symptoms can be concerning, they do not directly point to internal carotid artery involvement as clearly as a facial droop does.