EEGs cannot assure that someone is seizure free. EEGs can only rule in. A negative reading means that seizures weren't occurring at the time of the test or that they were occurring too deep in the brain to register. It may be that the person never has seizure activity, but an EEG won't prove that.Sammy had seizures when he was 11 days old. He has had EEGS to follow up and make sure he is seizure free....
Neither I nor my son nor my friend who has had seizures for 50 years ever had an EEG that indicated seizure activity yet we all have/had temporal lobe epilepsy. (I say "had" because I have been seizure free off medication for 15 years.)
Considering that your son's behavior could be caused by partial seizure activity and anti-convulsants have been tested on and approved for children, it seems odd that the neurologist wants to try an anti-hypertensive rather than an anti-convulsant.