A 3-year-old girl with mitral valve prolapse is cyanotic. What is the most appropriate immediate intervention?

In the scenario presented, providing oxygen by nasal cannula is the most appropriate immediate intervention for a cyanotic child. Cyanosis indicates that the body is not receiving enough oxygen, which is critical, especially in a child with a known heart condition like mitral valve prolapse. Administering oxygen helps to increase the oxygen saturation in the blood, improving tissue perfusion and addressing the immediate needs of the child.

When considering the other options, nitroglycerin is generally used to relieve chest pain and manage angina, specifically in adult populations with heart conditions, and may not be appropriate in this pediatric case. A non-rebreather mask could provide higher concentrations of oxygen than a nasal cannula and might be considered in some emergency scenarios, but for a child and particularly in this context, a nasal cannula is often sufficient and less cumbersome. Aspirin is an antiplatelet medication and is generally used for cardiac events in adults; it does not directly help with oxygenation in an acute setting involving cyanosis in a child.

Thus, providing oxygen by nasal cannula is the most suitable approach to manage the immediate need for increased oxygenation in this situation.