Here is what you did absolutely right, and that is you had your med checked by your buddy.
We all make errors, and in the heat of the moment, "50" of anything would be easily confused. (Hence why verbal orders in a non-emergency settiing are more and more discouraged--if the doc can say it, they can write it) It is a hard thing to have them do, though.
In any event, make sure going forward that you ask for clarification (ie: do you mean mgs per kg) and be sure that you know what a "safe dose" of commonly used medications would be--so if it doesn't "sound" right, use your resources and look it up.
This patient had a great deal of anxiety for some time, therefore, you looking up the med, and checking math with another nurse wouldn't have delayed care beyond a "reasonable" time frame. Do not ever get into a position where you say "ah, well, I should've but I didn't." Just don't until you are certain.
So now you know. And I assume that this wasn't your last day with your buddy--so I wouldn't sweat it, but I would use it to change your practice. And that is a good thing. If your buddy or the MD says anything to you, I would simply say "Now I know, it will not happen again, I have learned from it, and moving forward I will be mindful".
Further, and I have no idea if this is policy anywhere else, is there a reason you do not check your dose and math with a second nurse anyways? I know in my experience, and granted it is not PICU, however, we had to have a second nurse check if we were altering a dose of medication from the intended dose, or the dispensed dose (ie: 50 mgs per kg or if the vial was labeled 50mgs per 5ml and you only needed 20mgs or something of that nature).
You got this, and best wishes.