A 52-year-old woman with rheumatoid arthritis on methotrexate and prednisolone presents with acute onset of right hip pain, fever (39.2°C), and inability to walk. Hip aspiration yields synovial fluid with WBC 72,000/μL (92% neutrophils), glucose 22 mg/dL (serum 115 mg/dL), protein 5.8 g/dL, and negative Gram stain. Blood cultures are pending. She is allergic to penicillin (rash). What is the most appropriate immediate management?