A 22-year-old woman presents with a 4-day history of sore throat, fever (38.5°C), and dysphagia. On examination, she has bilateral tonsillar enlargement with yellowish exudate, cervical lymphadenopathy, and no trismus or uvular deviation. Rapid antigen detection test (RADT) for Group A Streptococcus is positive. She has no penicillin allergy. What is the most appropriate immediate management?