Final answer:
The most appropriate next step is supportive care.
Step-by-step explanation:
The most appropriate next step for this patient is D. Supportive care.
The patient is presenting with acute swelling of the cheek, which worsens with meals. Examination reveals an erythematous and edematous tender parotid duct, and purulent material is expressed with massage. These findings suggest that the patient likely has a parotid abscess or parotitis.
The initial management of a parotid abscess or parotitis usually involves supportive care, which includes warm compresses, adequate hydration, pain control, and also offering the patient soft, non-acidic foods.