Viral Upper Respiratory Tract Infection (URTI): This is the most common cause of runny nose and cough in infants, often caused by viruses such as rhinovirus, coronavirus, or adenovirus. The absence of fever and the age of the patient make this diagnosis highly plausible.

Allergic Rhinitis: Although less common in infants, allergic reactions to environmental allergens can cause runny nose and cough. This could be considered, especially if there's a family history of allergies or if symptoms persist or recur.
Exposure to Irritants: Exposure to smoke, pollution, or strong odors can irritate the nasal passages and cause coughing in infants.
Gastroesophageal Reflux Disease (GERD): GERD can cause coughing due to the reflux of stomach contents into the esophagus, irritating the throat.

Congenital Heart Disease: Although rare, congenital heart diseases can present with respiratory symptoms due to pulmonary congestion. A thorough examination and possibly an echocardiogram might be warranted if other signs are present.
Cystic Fibrosis: This genetic disorder can lead to recurrent respiratory infections and should be considered if the infant has persistent or severe symptoms.
Inborn Errors of Metabolism: Certain metabolic disorders can present with nonspecific symptoms, including respiratory issues. These are rare but critical to diagnose early.

Primary Ciliary Dyskinesia (Kartagener Syndrome): A rare genetic disorder affecting the cilia, leading to chronic respiratory infections and other systemic issues.
Immune Deficiency: Conditions like SCID (Severe Combined Immunodeficiency) can present with recurrent or severe infections, including respiratory ones, although these are extremely rare.
Anatomical Abnormalities: Such as choanal atresia or other congenital anomalies of the respiratory tract, which can cause respiratory symptoms in infants.