As an ex dental hospital frau
. Students do work on you at a teaching hospital but they are supervised and have each part of treatment checked regularly. A root canal appointment could last 3 hours at a teaching hospital, whereas it would take half that in a regular dentist. The work is checked over by the best dentists in the business though, we had several professors at ours that were very highly regarded.
We only took emergency cases that were not registered with a dentist already, so Jack wouldn't qualify so she would be sent back to her own dentist for treatment. She could be referred to the hospital if the problem required surgery or was complex, but this takes time.
However, we would see any patient with a swollen face (industry term being "fat face") and the policy at that time was that no dentist could turn away a patient with facial swelling, so if you are ever in pain and the dentist can't see you - tell them you think your cheek/jaw is swollen and they have a duty of care to see you immediately.