How common is it for children to throw up after having a nightmare?

It is not uncommon: Small children vomits often whenever they are sick, upset, stressed out, or even very tired. I believe that vomiting is a stress reaction, and thus vomiting in small children does not necessarily mean that they have gastrointestinal problems. However recurrent nighmares associated with repetitive vomiting needs to be investigated by a pediatrician to exclude any organic causes.

Nightmares: It is not common, but may be caused by the dreams. Please also have your pediatrician do a full exam and they may consider a sleep study. But be sure your child is not under some severe distress. When bad things happen we are going to have disturbing dreams that could cause the nausea.