It makes sense to be careful about identifying physical symptoms as having psychological roots, but that does seem to be the case with your son. Some children display separation anxiety to such a point that the physical manifestations of the anxiety become pronounced. One typical response to anxiety or stress is for the stomach to produce acids which in turn prompt the vomiting. If your son's physical symptoms are strongly related to the experiences you describe, an evaluation by a pediatric mental health or behavioral health practitioner would make sense.