my dog has a broken nail now also, but not as bad as your dog's
his is cracked down the side down the length of the entire nail. vet told me to use antibiotics for what looked like mild infection, and pain meds. so along the same lines
my dog never favored his, but i can imagine that as the nail starts to grow back in it could be painful - youre probably right to wait a few days and head back to the vet.
you could even call them and ask if you should be worried or if its something normal for that type of injury.