Vomiting is an occurrence seen in Bully.
Sometimes, students can be seen vomiting on campus in certain areas such as outside the biology classroom, near the fountain and at the path infront of the main building which leads to the parking lot. Students can also be seen vomiting at the carnival. Adults are also seen vomiting, albeit rarely. An example is in the mission Cook's Crush, where the hobo Handy vomits after Jimmy takes away his sedatives. Characters actually have dialogue specifically for when they see someone else vomit.
Most notably, Mandy vomits after a stink bomb falls out of her locker (courtesy of Jimmy) in That Bitch, and Kirby vomits during the mission The Big Game after drinking the sports drink tainted with Jimmy's urine.
When Jimmy is forced to see Dr. Crabblesnitch after being busted, one of the things Crabblesnitch may accuse him of doing is making another student vomit. However, currently there aren't any known reliable methods to make somebody vomit. They will occasionally vomit if hit with a stink bomb.
Jimmy can't vomit under most circumstances, but he may vomit if he rides on the rides at Billy Crane's Traveling Carnival too many times in a row.