Jaybay and peekawho always give good advice. Thank you Jaybay and peekawho!
It is important to take her back to the vet. Since you have just taken her to the vet, your vet will probably only charge for a recheck (less than an initial office visit), or will not charge you at all for the exam. You will just be responsible for the medications or any tests performed. I add this information about fees since I do get a lot of cost questions.
The vet will be able to do things that you cannot do at home such as take her temperature, check her blood glucose, since puppies do get hypoglycemic very easily, check for common and less common parasites, make sure she has no heart murmur or other congenital abnormalitits, etc, etc. Vomiting and not eating are not normal in puppies. It could be something as simple as intestinal parasites. A normal fecal analysis will show common parasites, but I will always do an additional check for Giardia L., a protozoal parasite. Even if the breeder has given the puppy Strongid, or Pyrantal, or Nemex, I will check for parasites and even if none are seen I will treat just in case. Approximately 99% of all parents pass parasites to their offspring. Many parasites pass through the placenta in vitro.
I often also do a urinalysis, since even young puppies can get urinary tract infections which can make it even more difficult to house train, though they are usually older than 8 weeks old.
A congenital problem called collapsing trachea can cause a pet to cough so hard that they vomit, and this must also be checked by your vet.
I am only listing some common possibilities, out of literally hundreds of them.
A puppy who doesn't eat will get hypoglycemia so don't wait too long to get professional help. Your puppy may have to stay overnight if she needs to be force fed or needs fluid therapy. Let us know how it turns out and good luck!
Please read through the post titled, "The 5th Puppy Just Died" on this board. The poster lost nearly an entire litter of shih tzu pups because they weren't kept warm enough. Apparently they need to be kept about 85 degrees to maintain normal digestive function. You still need to have a vet take a look at her though.
An 8 week old small breed puppy can get very, very sick in the blink of an eye.
Personally, I would let the vet know that she is still not eating and get his/her advice right away.
While a pup may be a little homesick for the first day or two, I do not think that repeated vomiting is normal, and I'd be quite worried.