Viral upper respiratory tract infection: This is the most common cause of a dry cough in a child of this age, often due to viruses such as rhinovirus, coronavirus, or adenovirus. The child being otherwise well supports this diagnosis, as viral infections can cause cough without severe systemic symptoms.

Asthma: Although the child is otherwise well, asthma can present with cough as a sole symptom, especially in young children. It's a common condition in pediatric populations and should be considered, especially if there's a family history or if the cough is worsening over time.
Allergic rhinitis: Allergies can cause a dry cough due to postnasal drip. If the child is exposed to allergens and has other symptoms like sneezing or runny nose, this could be a likely diagnosis.
Gastroesophageal reflux disease (GERD): GERD can cause a dry cough in children due to the irritation of the esophagus and subsequent aspiration of stomach contents into the lungs. This is more likely if the child has symptoms like vomiting or if the cough worsens after feeding.

Pertussis (Whooping Cough): Although less common due to vaccination, pertussis can still occur, especially in areas with low vaccination rates or in children who have not completed their vaccination series. It's crucial to consider this diagnosis due to its potential severity and the need for public health intervention.
Tuberculosis (TB): TB is a critical diagnosis not to miss, especially if the child has been exposed to someone with TB or has recently traveled to an area with high TB prevalence. A dry cough can be an early symptom of pulmonary TB.
Foreign body aspiration: This is an emergency that requires immediate attention. If a child has aspirated a foreign body, it can cause a sudden onset of cough, among other symptoms. The history might reveal an incident of choking or an object going down the wrong way.

Cystic fibrosis: This genetic disorder can cause chronic respiratory symptoms, including a dry cough, due to the production of thick, sticky mucus. It's rare but should be considered if the child has recurrent respiratory infections or other symptoms like failure to thrive.
Primary ciliary dyskinesia: A rare genetic disorder that affects the function of cilia in the respiratory tract, leading to chronic respiratory infections and cough.
Interstitial lung disease: A broad category of rare diseases affecting the lung tissue, which can cause a dry cough among other symptoms like difficulty breathing.