She needs to be seen by a vet ASAP. It would be good to take a stool specimen with you when you go. Puppies this young can become dehydrated easily and diarrhea is nothing to mess with. They also can become hypoglycemic.
As for the choking sound, it sounds like it may be a reverse sneeze which is really not an emergency. Sometimes you can stop it by holding your fingers over the nose....or by gently rubbing the throat. I will post a video below of it. If you can, get a video of her doing it to show the vet when you go.
Please let us know how things are going. Welcome to Yorkie Talk.
