If they are white lines and few inches long they are round worms. Many many puppies have round worms..i had a 1 week old puppy vomit a mess that looked bigger than her poor little stomach. Your vet should be able to check a stool sample and tell you what you need to do. It is an easy fix, but must be done soon. I am glad to hear that it is something like that and not a sponge or foam, or swelled up dry food. There is good info on good puppy diet on this forum..i would switch from Purina.