You already probably know that mixing the two, dextromethorhpan or Delsym and ethanol (alcohol) wasn't the best course of action. People do it, though, and most do not suffer any serious or life-threatening reactions.
Delsym's common side effects are nausea, dizziness, abdominal pain, drowsiness and fatigue
. Having said that, both Delsym and alcohol are heavily metabolized by liver. When you use both there is a bit of competition and your liver gets overwhelmed. Consuming too much alcohol can cause nausea and vomiting as well, so her symptoms are even worse because of that. Frequent consumption of alcohol can cause fatty liver or even lead to hepatitis due to ethanol.
Since she has been vomiting a lot, there is increased intra-abdominal (inside the abdomen) pressure which makes the bile, which is secreted downstream from the stomach, reflux into the stomach and then into the esophagus - that is why her vomit looks green. She should stay well-hydrated to compensate for all the fluid loss.
She will probably be OK and feel better soon. However, if she has pain in the right side just under her rib cage, if she develops fever, her nausea, vomiting and diarrhea continues, she should see a doctor.