I've taken the recommended dose for adults myself and it completely knocks me out to the point I can't open my eyes even if I want too, comatosed almost hehe so for me I wouldn't give it to my dd in case she had the same reaction.
My mum has said to me why don't you give dd some phenergan to break her terrible sleeping patterns but there's just no way I would give it to her, seems it was common practice 20ish yrs ago to give babies phenergan to help them sleep.
It's strange the dr prescribed it. I think if bub is sick with a cold, breathing would already be a bit of a struggle and giving them phenergan when like this there would be even more of a risk of them stopping breathing.