If he us throwing up worms then he has a bad infestation and that needs to be taken care if ASAP!! Completely agree with Karla that you get a good medication from the Vet.
If you haven't had it done, your pup should be checked by the Vet and put on a puppy plan for wormings and a 'full" series of shots! You don't want to lose your puppy to Parvo! When you go to the Vet, and hope you do, take a fresh stool sample in with you to be checked. Put it in a baggie or clean plastic container.
Yes, go to your vet.
Worms can be fatal in puppies who get this sick.
Yes, They can make him very sick & sometimes fatal....You need to get to your Vet and get a worming medicine for this guy.....The prescription ones from your Vet WILL work.....OTC ones from the store not only DON'T work, they are also very dangerous....Don't risk it.....Your Vet has the best wormers...You'll need to take a fecal sample with you to the Vet so they can determine which kind of worms to treat.....Good luck, Karla