Which client should the postpartum nurse see first after receiving handoff report?

The most critical client for the postpartum nurse to see first is the mother experiencing heavy bleeding. This situation is urgent as heavy postpartum bleeding can lead to severe complications, including hypovolemic shock and maternal death if not addressed promptly. Any significant bleeding after childbirth is a potential emergency that requires immediate assessment and intervention to stabilize the mother's condition.

While the other options present concerns that also need to be addressed, they do not carry the same level of urgency. A bilirubin reading of 8.6 mg/dL in a term infant is elevated, but it is not typically urgent unless it exceeds critical thresholds or if the infant shows symptoms of jaundice. The infant requiring routine vaccinations should be managed but does not need immediate attention. Lastly, signs of infection in the mother are serious and warrant follow-up, but heavy bleeding takes precedence as it can quickly deteriorate the mother's health.

In summary, the need for immediate intervention in cases of heavy postpartum bleeding makes this situation the highest priority for the nurse.