Several things in your post concern me.

The first being a puppy is acting lethargic, not eating, and vomiting. That is not normal puppy behaviour. This could be anything from switching foods, to adjusting to a new environment to coming down with parvo which can take a while to show up after being exposed to it. In any case a vet check up is certainly warranted. Be sure to take a fresh stool sample with you and they can check for worms and the like.

The second being you mentioned was she has been eating toys and carpet. This can not only upset the tummy, but sometimes can cause blockages that are very serious. Again a vet check is certainly warranted. Be sure to tell them she eats things she shouldn't have.

The third was the trip to PetSmart. Unless I misread your post (and please forgive me if I did) that this new puppy has not had all the series of the vaccinations yet? If that is the case please resist the urge to take your puppy to public areas with other dogs (ei: pet stores, dog parks etc). Your puppy is NOT protected from those diseases until a few weeks AFTER the LAST vaccination in the series. Being a young animal they are more succeptable (sp?) to picking things up, particularly if they are already sick or have an immune system already fighting off a bug.

In any case your post has a few red flags that should be checked out with a vet. They may not be anything serious but it would be enough to warrant spending a few $$ on having things checked out to be sure. The vet should be able to give you the cost of at least the checkup and fecal test prices over the phone when you make an appointment. Let them know when you get there that you need to know prices before they do anything extra, that way you don't get sticker shock or something at the check out counter. Not all vet visits cost $$$$. Some things are amazingly inexpensive and simple.

Keep us posted as to what goes on with your puppy, and post a few pix of your new little bundle of fur also.