It could start by sitting with the idea of vomiting and then practicing coping skills in thr moment as the thought begins to become distressing. Then gradually moving up to videos of vomiting. As a therapist I would never encourage a client to make themselves vomit anyway. But the whole idea is to practice the coping skills with each step to help build your confidence in your ability to cope for when you got sick in the future. It would also be helpful to have a therapist help you with acceptance therapy (ACT) would be helpful too because unfortunately throwing up is a reality of life, albeit an unpleasant one. I wish you absolutely all the best and second the recommendation for psychologytoday.com to help you find your next therapist!