A 28-year-old woman presents to an outpatient clinic with a 5-day history of progressively worsening left ear pain, fever, and a dull headache. She reports a recent upper respiratory infection followed by an acute ear infection that did not fully resolve with prior treatment. On examination, the left auricle is displaced inferiorly and anteriorly, with significant tenderness and fluctuance noted over the mastoid process. The external auditory canal is edematous, and the tympanic membrane is obscured by purulent discharge. Her temperature is 38.9 degrees C, heart rate 98/min, and blood pressure 118/72 mmHg. Laboratory results indicate a White Blood Cell count of 16.5 x 10^9/L, C-reactive protein of 95 mg/L, and an Erythrocyte Sedimentation Rate of 60 mm/hr. What is the most likely diagnosis and the critical next step in management, considering potential complications?