Final answer:
The nurse should inform the mother that the red and swollen umbilical cord site is normal and will resolve on its own. It is important to keep the area clean and dry, but antibiotic ointment is not needed unless there are signs of infection.
Step-by-step explanation:
The nurse should tell the mother that the red and swollen umbilical cord site is normal and will resolve on its own. The umbilical cord stub goes through a natural process of drying out, shriveling, darkening, and falling off within about three weeks of birth, after which it becomes the navel. It is important for the mother to keep the area clean and dry to prevent infection, but applying antibiotic ointment is not necessary unless there are signs of infection such as pus or increasing redness, swelling, and pain.