Recurrent Respiratory Infection: Given the history of tracheoesophageal fistula, these children are prone to recurrent respiratory infections due to potential aspiration and anatomical abnormalities. The symptoms of mild hypoxia, cough, and noisy breathing are consistent with a respiratory infection.

Asthma: Noisy breathing and cough could be indicative of asthma, especially if the child has a history of atopic diseases or if there's a family history of asthma.
Reactive Airway Disease: Similar to asthma, this condition could cause the symptoms described, especially in a child with a history that might predispose them to respiratory issues.
Gastroesophageal Reflux Disease (GERD): Children with a history of tracheoesophageal fistula are at risk for GERD, which can cause respiratory symptoms due to aspiration of gastric contents.

Foreign Body Aspiration: Although less common in a 4-year-old compared to a toddler, aspiration of a foreign body can cause sudden onset of respiratory symptoms, including cough and noisy breathing, and is potentially life-threatening.
Pneumonia: Bacterial pneumonia could present with these symptoms and is a serious condition that requires prompt treatment.
Anaphylaxis: Though rare, anaphylaxis can cause respiratory distress and is a medical emergency.

Tracheomalacia: A condition where the trachea is soft and collapsible, which can cause noisy breathing and respiratory distress. It's more common in children with a history of tracheoesophageal fistula.
Bronchiolitis Obliterans: A rare condition that can occur after a severe respiratory infection, leading to chronic respiratory symptoms.
Congenital or Acquired Laryngeal Lesions: Such as laryngomalacia or vocal cord paralysis, which could cause noisy breathing but are less likely given the context of the other symptoms.