Go through these in order and stop at the first one that applies. If you are reading this for someone else, answer for them.
Follow the emergency instructions provided by your local healthcare service.
Seek emergency help if bleeding is heavy or does not stop with gentle pressure, your baby is difficult to wake, has trouble breathing, looks blue or grey, has a seizure, or appears severely unwell.
Arrange prompt, same-day medical advice if redness is spreading beyond the belly button, the skin is swollen or warm, pus is present, there is a strong foul smell, or the area appears painful.
Also call promptly for repeated bleeding, persistent drainage, poor feeding, vomiting, or unusual sleepiness.
A temperature of 38°C or 100.4°F or higher in a baby younger than 3 months needs urgent medical assessment.
A tiny spot of blood when the stump separates, without ongoing bleeding or illness, can usually be discussed at routine follow-up.
A small moist lump after separation also usually needs a routine appointment unless there are signs of infection.
Every sign above is quoted from the sofidex article on Umbilical cord care in newborns. If you are not sure, err upward — it is always reasonable to be checked.