Vomitting from a hairball usually looks very different from vomitting for other reasons, and it's often done when the cat has not eaten. Most of my cats get rid of hairballs by stretching out their necks, gagging a lot, walking backward and bringing up stomach fluids before the hairball itself. I'm sorry that your parents are not willing to take your cat to a vet since that is part and parcel of taking care of a pet. Please let us know how your cat is doing since we will worry about her.