Hi welcome to Health care magic forum.
Thanks for choosing H.C.M.F.
As you describe your son had stomach pain near his belly button. Nothing fault found in stools, urine, and blood.
Most probably the condition is intestinal worms, or lactose intolarance, confirmed by reducing substances inthe stools, may be school sick ness. The brown vomiting
could be due to oozing of blood due to severe gastric irritation.
I advise you to consult a pediatrician
for diagnosis and treatment.
Wishing for a quick and complete recovery.