Thank you for your query.
If the stools tests do not show any blood then the child might have a polyp/fissure which is bleeding when he is passing hard stool.
Give him a stool softener
and consult a pediatric surgeon for the fissure/polyp if any.
If you have any further queries you are free to consult me.
Hope this answers your query.
Wishing a speedy recovery.
Have a nice day.