Wendy, to me your and 'your medics' tx, assessment and advice sounds perfectly reasonable. This being said, "God" has a point about the bleeding into the esophagus. Since there is blood in the oral cavity or pharynx and blood is highly irritant on the stomach often causing nausea/vomiting it may not be prudent to assume the child was feeling ill due to medication side effects. My point in saying this is just that there were signs present indicating there may have been more to the pt's presentation.
I can only speak for myself on the original topic. I have never "talked someone out" of going to the hospital. Even if I though it was unnecessary or an abuse of the system, even if I had not had a break or eaten yet that day, even if it was four o’clock in the morning. I have on the other hand, made sure that the pt and pts family are making an informed decision in regards to their treatment options. This IS my responsibility as a medic.