A 6-year-old unvaccinated boy from rural Maharashtra presents with a 3-day history of sore throat, low-grade fever (38.2°C), and progressive difficulty swallowing. On examination, he has a thick, adherent, greyish-white membrane covering both tonsils and extending into the pharynx. The membrane does not blanch on scraping and bleeds when forcefully removed. He also has cervical lymphadenopathy with mild neck edema. His respiratory rate is 28/min and heart rate is 110/min. What is the most likely diagnosis and the single most important immediate intervention?