Don't get this poor boy a puppy!
One of my DGC was knocked flying when she was about 2 by a over-friendly dog and has been nervous since then. They have got a puppy many years later and she adores him, but that doesn't mean to say she would like every dog and quite rightly. Not all dogs are lovely and friendly and children should be taught that.
This is the noise, I think, which I can well understand although I find a constantly yapping dog annoying not frightening.
Dogs are everywhere, lovely, yappy, frightening and having a constant fear of them and their barking and sudden movements is something which this boy needs help with.
What about those neat little earplugs for the time being, perhaps playing some gentle music?
you do not need to own these or any dogs.
you can pay a dog trainer to help.
It's the owners who need training.
If they are really aggressive they need to be kept under control.