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They could mean a cold or allergy.

(HealthDay News) — 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.

Source: http://www.healthfinder.gov/news/newsstory.aspx?Docid=670734&source=govdelivery