Your baby’s umbilical cord will fall off by itself in 1 to 4 weeks. Until it does, apply alcohol on a cotton swab to the cord three times a day. If the navel oozes spots of blood or a clear moist fluid for a while after the cord drops off, don’t worry. This is natural. But if the oozing persists more than 2 days, if the discharge smells particularly bad, if the skin around the cord gets red, or if your baby gets a fever, notify our office.