I was sick just recently (but it wasn't ''much'') and it wasn't terrifying like I thought it would be. Still scary and unpleasant and I hope it doesn't happen again for a looooong time, but..
You do NOT need to vomit to get over your fear. If you aren't willing to go through with doing that and are forced into being sick; it will only make this phobia worse. I think exposure to vomit is a much safer way to cure this fear. Watching videos of people being sick and/or hearing it etc...gradually working your way up to being able to sit and watch it without freaking out. I would question this doctors professionalism because it is NOT something you have to put yourself through.