Viral Upper Respiratory Tract Infection (URTI): This is the most common cause of cough and low-grade fever in infants, often caused by viruses such as rhinovirus, coronavirus, or respiratory syncytial virus (RSV). The age of the patient and the symptoms presented align well with this diagnosis.

Bronchiolitis: Common in infants, especially those under 6 months, caused by RSV and other viruses. It presents with cough, wheezing, and sometimes fever.
Pneumonia: Can be caused by viral or bacterial pathogens. Symptoms include cough, fever, and can progress to more severe respiratory distress.
Influenza: Though seasonal, influenza can cause cough and fever in infants and is a significant concern due to the potential for severe disease.

Pertussis (Whooping Cough): A bacterial infection that can cause severe coughing fits, especially in infants who may not have completed their vaccination series. It's crucial to consider this diagnosis due to its potential severity and the need for prompt treatment.
Congenital Heart Disease with Respiratory Infection: Infants with undiagnosed congenital heart disease may present with worsening symptoms during a respiratory infection, making it critical to consider in the differential.
Severe Combined Immunodeficiency (SCID): Infants with SCID may present with recurrent or severe infections, including respiratory infections that do not resolve as expected.

Cystic Fibrosis: A genetic disorder that can lead to recurrent respiratory infections, among other symptoms. While rare, it's an important consideration in infants with persistent or severe respiratory symptoms.
Foreign Body Aspiration: Though more common in toddlers, it's possible in infants, especially if they have been exposed to small objects they might put in their mouths.
Tuberculosis (TB): Uncommon in infants in many parts of the world but critical to consider, especially if there's a known exposure history or if the infant is from a region with high TB prevalence.