When you need to. This is a very broad question. Bottom line is you need to call when you have concerns/ are worried. As new parents, you need support and many times just education. Your doctor's office is the best place to start. Some things are common sense...Fevers over 104, bleeding that won't stop, head injury with loss of consciousness, excessive vomiting or diarrhea. Relax. You know when to call.
Serious Illness. You hopefully feel you can call your pediatrician with any concern but there are a number of signs of serious illness that are important to report right away. These would include an infant or child in severe unrelenting pain or that is inconsolable, lethargic to the point of being difficult to arouse, fever over 104.5, vomiting that is severe/unrelenting or bilious(green), labored breathing .