They could mean a cold or allergy

Nosebleeds are common during childhood, especially during the preschool years. Though they can be scary, they usually aren’t caused by a serious problem.

The American Academy of Pediatrics says common causes of nosebleeds include:

  - Allergies or a cold, which can lead to nasal swelling or irritation.
  - Trauma to the nose, from blowing too hard, picking or putting an object in the nose.
  - Exposure to a very dry environment or harsh fumes.
  - An abnormal anatomical structure of the nose.
  - An abnormal growth inside the nose.
  - A blood-clotting problem.
  - Taking medication that dries out the nasal passages.