My boy had worms tape worms when he was around 12 weeks....we think he got it from the lake the first time we took him...he ate sand that probably had fleas in it.
The vet gave him Drontal & it cleared fast. But you have to get your pup to the vet right away worms can cause a lot grief to the body. Bring a stool sample....if you can't the vet will have to take your word that you indeed saw worms.
Glad you talked to the vet. My 9 week old pooped out some large roundworms after being dewormed. Vet said he was just flushing them out but in a couple weeks he should be dewormed again. Might want to see if your vet recommends the same thing