A 38-year-old man from rural Maharashtra presents to the emergency department with a 3-day history of severe left knee pain, swelling, and inability to bear weight. He has a fever of 38.9°C and reports a puncture wound to the knee from a contaminated nail 5 days ago. On examination, the knee is grossly swollen, warm, and tender; passive range of motion is severely restricted. Synovial fluid analysis shows WBC 85,000/μL (95% neutrophils), protein 6.2 g/dL, glucose 18 mg/dL (serum glucose 110 mg/dL), and Gram stain shows Gram-positive cocci in clusters. What is the most appropriate next step in management?