Viral upper respiratory infection: This is the most likely diagnosis due to the common presentation of viral infections in this age group, characterized by fever, cough, and the radiographic findings of prominent lung markings and mild perihilar peribronchial wall thickening without consolidation or pleural effusion.

Bronchiolitis: Supported by guidelines from the Thoracic Society of Australia and New Zealand and PREDICT, which indicate that bronchiolitis can present with fever, cough, and peribronchial wall thickening, aligning well with the clinical presentation.
Pneumonia: Although there's no discrete consolidation, pneumonia can present with prominent lung markings and peribronchial thickening, along with fever and cough, as noted by the Royal Children's Hospital guidelines.
Asthma exacerbation: While less likely due to the absence of wheezing, it's still a consideration given the presentation of cough and increased lung markings, as described by the Australian and New Zealand Committee on Resuscitation guidelines.
Croup: Although typical presentations include a barking cough and stridor, which are not noted here, the Royal Children's Hospital guidelines mention fever and cough as part of the croup presentation.

Bacterial pneumonia: It's crucial to rule out bacterial pneumonia due to its potential severity. Diagnostic considerations should include a full blood examination (FBE), blood cultures, and acute phase reactants like CRP and procalcitonin, as per the Royal Children's Hospital guidelines.

Other infectious causes: Such as mycoplasma pneumonia, which can present similarly but is less common in this age group.
Immunodeficiency-related infections: In cases where the child has a known or suspected immunodeficiency, opportunistic infections could be considered.
Congenital heart disease with pulmonary overcirculation: Though less likely, conditions leading to increased pulmonary blood flow could present with similar radiographic findings.