Final answer:
The most appropriate initial step in the management of this patient is to administer antibiotic therapy, specifically azithromycin.
Step-by-step explanation:
The most appropriate initial step in the management of this patient is to administer antibiotic therapy. Based on the patient's symptoms and physical examination findings, it is likely that she has a bacterial respiratory infection such as pneumonia. Antibiotics are the mainstay of treatment for bacterial respiratory infections. The choice of antibiotic should be guided by the likely pathogens involved, which are typically Streptococcus pneumoniae, Haemophilus influenzae, or atypical pathogens such as Mycoplasma pneumoniae or Chlamydophila pneumoniae. In this case, based on the patient's age and symptoms, a good initial choice would be azithromycin, as it covers both typical and atypical pathogens.