Yes dogs can develop gastrointestinal upset (vomiting and/or diarrhea) from medications.  Without knowing what she was given (the shot) or what she is not now I can't comment on if these particular medications often cause vomiting.  I would contact the veterinarian who saw this dog for their opinion to make sure this is not anything serious.
To calm the stomach withhold food for 12 hours, allow access to small amounts of water, and then slowly reintroduce food.  A bland diet is ideal--boiled chicken, boiled rice.  You can also try given Pepcid--the dose is 0.5 milligrams per kilogram of body weight given by mouth twice daily.
If she continues vomiting she needs to be examined by a veterinarian.