A 28-year-old woman with known Graves' disease, currently on methimazole 15 mg daily, presents to the emergency department with fever (39.2°C), severe sore throat, and malaise of 2 days' duration. On examination, she appears unwell with pharyngeal erythema and cervical lymphadenopathy. Complete blood count shows WBC 1.8 × 10⁹/L (normal 4.5–11.0) with neutrophils 45% (normal 50–70%). Thyroid function tests show TSH 2.1 mIU/L and free T4 12.5 pmol/L (both normal range). What is the most appropriate immediate management?