S. -- You aren't doing anything wrong! Hyperactive kids are like that, although the bullying isn't necessarily a part of the behavior. Maybe he gets disgusted with people who seem slow to him and he shows it with aggression. Maybe. I would seriously consider taking him to a child psychiatrist. I expect your pediatrician can suggest a good one.
Often caffeine quiets down hyperactive kids. You could try giving him sugar-free caffeinated soft drinks. If that helps, great, but see the child psychiatrist too!
While your child is this young it's your responsibility to do what you can to help him control his behavior. But don't get in the habit! The older he becomes the more his behavior will be his responsibility. Even while he's young don't shield him from the consequences of his actions. If the other kids shun him or someone "aggresses" back at him, don't go to his defense! Just try to help him see how his behavior contributes to the situation.
This is what I did when my kids acted out. I'm not sure if it's do-able with a hyper child, but here it is: When one or more of them misbehaved I would make all the"perpetrators" take time out for 5 minutes. I'd set the timer to ring in 5 minutes and then I'd sit them in kitchen chairs facing a blank wall and up close to it -- the idea being that there is nothing to do but sit there and think. Then I'd tell them that the 5 minutes are punishment for what they did, and that when the bell rings if they think they can behave in a civilized manner and treat each other like human beings they may leave their chairs and resume playing. On the other hand, if they don't think they're ready to be civilized yet, then they have to stay on the chair until they think they can be. Then they, too, can resume play. I also tell them that if they think they can be civilized but it turns out that they can't, I will SADLY have to return them to their chair for SIX minutes and repeat the whole process. I never once had a child who wasn't ready to be civilized when that bell rang! You didn't say how old your other children are, and this certainly wouldn't work with younger kids, but if they're older or if your son has a friend over and starts misbehaving, this can be useful.
I wish you and your family the very best --
L.