as per the details u have given,
medically it known as EPISTAXIS
...but in case of children the most common cause of epistaxis is NASAL PICKING AND RUBBING..
so i suspect , this may be the reason for epistaxis,, but any way to rule out the other causes for epistaxis, the following tests should be run..
1. complete blood work including bleeding time
and clotting time.
and platelet count
2. ENT EXAMINATION TO RULE OUT ANY NASAL PROBLEM
after getting the above tests done, we can come to conclusion..
hope this will help u...