Your mother may be right. It is not advisable to start a child on antibiotics without confirming an infection.
Your brother needs to get a complete blood count
done along with widal test
and peripheral smear.
The management of fever
in an 8 years old kid is different. The cause had to be found out and treated accordingly.
In addition, we need to find the focus of infection that is causing the fever.
A chest x-ray may be required too.
Please take him back to his treating doctor and get these investigations done.
I wish your brother a speedy recovery.