Are there long-term effects of brain bleeding on my child's health?

It depends: First, what compartment was the blood in - subarachnoid, subdural, intraparenchymal (in the brain itself), intraventricular? Second, how much blood and what was the cause and what level or care did the child receive? Answers to these predict a range of lt effects from none to seizures to cognitive and/or comportmental abnormalities to hydrocephalus. And any of these issues can range in severity.

Yes and No: Infants with brain bleeds fall into several categories from mild to severe. The mildest form can have no long term effects but severe forms usually have long term effects.