Question

A $10$-week-old female infant is brought to the pediatric emergency department by her parents due to severe spells of coughing. The mother reports that the infant had a runny nose, mild cough, and tactile fever for about a week. Over the past $5$ days, the cough has worsened significantly, occurring in sudden, rapid bursts. During these episodes, the infant's face turns red, and she makes a high-pitched "whooping" sound when she finally catches her breath. She has vomited her formula after several of these coughing spells. The infant has not received any routine immunizations because the family recently immigrated. Vital signs between episodes are temperature $37.1^\circ\text{C}$ ($98.8^\circ\text{F}$), pulse $140$/min, and respirations $40$/min. Physical examination between coughing spells shows a well-appearing infant with clear lungs on auscultation. Laboratory studies reveal a leukocyte count of $24,000/\text{mm}^3$ with $72\%$ lymphocytes. Which of the following is the most appropriate next step in management?