Viral upper respiratory infection (URI): This is the most common cause of cough in infants, especially with an older sibling also being sick, suggesting a contagious etiology. The absence of fever and the ability to eat and drink normally further support this diagnosis.

Bronchiolitis: Common in infants, especially under 2 years, often caused by respiratory syncytial virus (RSV). The presentation can include cough, and while it might not always be accompanied by fever, the age and symptoms align.
Allergic rhinitis: Though less common in infants, exposure to allergens could cause chronic cough. However, this would typically be accompanied by other symptoms like nasal congestion or runny nose.
Gastroesophageal reflux disease (GERD): Can cause cough in infants due to acid reflux irritating the throat. The fact that the infant is eating and drinking without issue doesn't rule out GERD, as symptoms can be intermittent.

Pertussis (Whooping Cough): Although less likely due to vaccination, it's crucial not to miss this diagnosis, especially if the cough is severe or has a characteristic whoop. Vaccination status of the infant and siblings should be considered.
Pneumonia: While the infant is afebrile and eating/drinking normally, pneumonia can sometimes present atypically, especially in young children. A lack of respiratory distress or other concerning symptoms makes this less likely but not impossible.
Foreign body aspiration: This is an emergency that requires immediate attention. The history might not always be clear, but any suspicion warrants thorough investigation.

Cystic fibrosis: A genetic disorder that can lead to recurrent respiratory infections and chronic cough. It's rare and would typically be accompanied by other symptoms like failure to thrive or recurrent diarrhea.
Primary ciliary dyskinesia: A rare genetic disorder affecting the cilia, leading to chronic respiratory infections and cough. Other symptoms might include situs inversus or chronic otitis media.
Tuberculosis (TB): Extremely rare in infants without known exposure, but given the potential severity, it should be considered in the appropriate context, such as travel history or exposure to someone with TB.