I waited by the door and caught a kid ringing my doorbell
What did you do when you caught the kid?
I screamed at him, "You little brat! Get out of here! Go home!".
It is understandable to be upset with somebody for annoying you and you should hold them accountable for what they did, but they were a child and it would be better to tell the parents. That way the parents will hold them accountable for it and punish them.
The kid's parents will be the ones who brought a brat into the world. I'd like to yell at them too!
I'm not sure that yelling at someone is the solution in this situation. It'll probably make things very tense in your neighborhood. It's important to get along with your neighbors.