Hi there :) It sure sounds like you might have a trouble maker on your hands!!
While cotton balls aren't particularly exciting on the grand scheme of foreign body ingestions, we sometimes can have concern for what else may have been ingested at the same time or what the cotton balls may have contained (like nail polish remover, makeup remover, etc.) It'd be very unlikely for a handful of cotton balls to cause a GI obstruction, but not impossible. Often times if I have to do surgery on a dog with a history like that who is now obstructed, I usually find that the dog ALSO ate something else that was contributing to the obstruction. So by themselves, cotton balls aren't all that likely to cause a major issue.
With dogs who are vomiting, I generally begin with the same guidelines:
As long as their breathing is not labored, there is no abdominal distention, and their gums are pink and moist, I usually recommend holding off on giving any food or water for at least 6-8 hours. If they are continuing to vomit though this time, it's time to see the vet. If they stop vomiting, then I start by offering a small portion of water. If they keep that down for more than 2 hours, I offer another small amount of water and a small taste of food (1-2tsp). As long as they continue to tolerate small meals, you can gradually increase the amount of food at each sitting and increase the time in between meals. If they aren't eating at all for >24 hours, this also merits a trip to the vet.
Foreign body obstructions typically cause intractable vomiting - they are absolutely unable to keep anything down or they refuse to eat anything at all. I suspect that your pup will likely recover if the cotton balls were the only thing she ate that she wasn't supposed to eat ;) Please let me know what other questions I can answer for you :)
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