You should only give your child penicillin or any other drug after it has been prescribed to the child himself and not another person even if they have the same symptoms. Instead, take your son to the doctor for proper diagnosis to be made.
Make sure your son is prescribed the right medication for the illness he has. Antibiotics can be very bacteria specific. You also don't want to give your son too few antibiotics. This is one way antibiotic resistance gets started.