Dear scared, maybe this is what we call an Over-Valued Idea --- someting that one person takes far too serously. Most people find it a bit nauseating to see someone else vomiting, so that's hardly unusual.
But there's no point in letting oneself feel fearful of vomiting. After all, the body doesn't provide such mechanisms except with good reason. During human evolution, if we ate food which was poisonous or infected, it would end to make us feel nauseous, and we would vomit, ejecting the bad stuff from our body --- a pretty good idea. OK, sometimes, as with some viruses, they affect the part of the brain controlling vomiting and make us extra nauseous without there being anything in particular we need to get rid of in this way. But there's no harm in vomiting, and no good to be gained by struggling to prevent it from happening. Usually, though vomiting itself is an unpleasant experience, it produces great relief of the horrible feeling of nausea that precedes it.