Chances of rabies is rare a puppy throwing up is very common might be provost virus which is very common for puppy's. Unless the dog is showing other signs like foaming at the mouth, acting very aggressive, having problems with bright lights, walking funny, bumping in to walls and feeling very hot it's likely the puppy has just got a non human transferable virus. If your really worried I would take the puppy to the vet and call 911 for your mother because you have 48 hours to get the vaccine for rabies before it's to late.
Thank you for your advice. the puppy is fine now. what about the 10 days observation? if the puppy is alive and healthy after 10 days does my mother have to be vaccinated with anti rabies?