I'm so sorry to hear that your little granddaughter is having such trouble with eating. Infants can have reflux, and one of the symptoms can be vomiting. Generally, from what I understand, as long as the infant is gaining weight well, they just watch it and don't intervene. I do think your insistence on seeing a pediatrician about
the condition is the right course of action.
You may have already run across this website, but if not, you might find it helpful.digestive.niddk.nih.gov/ddiseases/pubs/gerdinfant/
I wish you the best of luck in finding an answer. Glad you've joined us! Hopefully other members will be by soon to share their own experiences.