Final answer:
The nurse should immediately follow up on cough and mild respiratory distress, singed nasal hairs and facial burns, and sooty sputum with increased heart rate due to potential airway damage and respiratory complications following smoke inhalation in the 4-year-old child.
Step-by-step explanation:
The nurse should identify that the following three findings require immediate follow-up in a 4-year-old child who was rescued from a home fire:
- Cough and mild respiratory distress
- Singed nasal hairs and facial burns
- Sooty sputum and increased heart rate
These symptoms suggest the child may have inhaled hot gases or smoke, potentially leading to airway damage and respiratory complications which could rapidly worsen. Thus, emergent assessment and intervention to support the airway, breathing, and circulation are critical.