Emetophobia - a phobia about vomiting. I had not been aware of this condition until a few years ago when nearly every month I had a new patient presenting with it. A typical case presentation is a school-age child who reports nausea and GI complaints and a fear of throwing up and starts to avoid situations and foods related to vomiting. Children will sometimes refuse to go to school if a child vomits in their class. Children will report nausea and decline to go to activities due to a fear of vomiting. Some children will sleep in the bathroom in case they throw up. Some children will avoid eating certain foods they perceive as related to getting sick and start checking dates on everything. Some children will restrict their diet to the point where they lose weight. The fear of contagion can lead some children to wash their hands to the point of raw skin. If the child actually is near a person vomiting or vomits themselves - a full-on panic attack can result. As you can see this is a condition that has a major impact on not just the child but also the whole family.
There are treatments for this condition. I often do schedule an appointment with a pediatric gastroenterologist to rule out medical conditions causing nausea or GI distress. For children with panic attack type symptoms and very high anxiety, I have successfully used fluoxetine to bring down the general level of arousal. This can make a child more amenable to therapy. Exposure-based CBT is an excellent way to work on this fear. There are books describing programs for this. A therapist works with the child to first be able to discuss vomiting, then perhaps look at a picture of someone vomiting, and up to maybe watching a video of someone vomiting. It takes time and patience but children can become desensitized to vomiting and be able to live their life again.
More info here: Emetophobia as expression of OCD