Respiratory Syncytial Virus (RSV) Infection: Given the age of the child, symptoms of fever, cough, and sputum, and the fact that the child has been in contact with peers (increasing the likelihood of viral transmission), RSV infection is a common cause of such symptoms in this age group, especially in a setting where the child has recently started showing symptoms after exposure.

Influenza: The child's symptoms and recent exposure to peers in a setting like Hyderabad, Telangana, India, where influenza can be prevalent, make this a plausible diagnosis. The fact that the child has been started on antiviral medication suggests that influenza was considered in the differential diagnosis.
Adenoviral Infection: Adenoviruses can cause a range of respiratory symptoms, including fever, cough, and sputum production, and are commonly seen in children, especially after exposure to other children.
Pneumococcal Pneumonia: Although the child has been started on amoxicillin-clavulanate, which would cover Streptococcus pneumoniae, the presence of lymphocytic predominance and the clinical presentation could still suggest a bacterial pneumonia, especially if the antiviral coverage was for a suspected viral infection that might have a bacterial superinfection.

Tuberculosis (TB): Given the location (Hyderabad, Telangana, India), where TB is more prevalent, and the symptoms of fever and cough, TB must be considered, especially if the child's condition does not improve with the current treatment or if there's a history of exposure to someone with TB.
Pneumocystis jirovecii Pneumonia (PCP): Although less common, PCP can present with similar symptoms and is particularly concerning in immunocompromised individuals. The lymphocytic predominance could suggest an opportunistic infection, but this would be less likely without a known immunocompromised state.
Severe Acute Respiratory Syndrome (SARS) or COVID-19: Given the current global situation, these viral infections must be considered, especially with symptoms of fever, cough, and exposure history, although the age and presentation might make these less likely than other viral causes.

Cytomegalovirus (CMV) Pneumonia: This would be more likely in an immunocompromised child, but given the lymphocytic predominance, it could be considered, especially if other diagnoses are ruled out.
Mycoplasma pneumoniae: Typically seen in older children and adolescents, but could be considered in this age group if other common causes are ruled out and the clinical presentation persists or worsens.