Every parent has been there — awake at 4am, watching their baby, not sure if what they are seeing is serious. Here is a clear framework.
Always call immediately or go to the ER: Baby under 3 months with fever above 38C. Difficulty breathing or blue lips. Unresponsive or extremely difficult to wake. Seizure. Signs of dehydration (no wet diaper for 8+ hours).
Call your doctor when they open: Fever lasting more than 3 days. Ear pulling with fever. Vomiting for more than 24 hours.
When in doubt, call. No pediatrician minds a worried parent calling — that is what they are there for.