A 28-year-old woman presents with a 3-day history of bilateral conjunctival injection, copious purulent discharge, and severe eye pain. On examination, she has chemosis, lid edema, and a thick mucopurulent exudate. Gram stain of the discharge shows gram-negative diplococci. She reports unprotected sexual contact 5 days ago. What is the most likely causative organism and the recommended first-line treatment?