What is causing this, and if we visit the doctor, should it be her pediatrician or an ophthalmologist?
I am waking up with swollen eyes lids very often. I am fighting my allergies since I was teenager. Maybe this is the same thing your daughter is suffering from.
Unfortunately the only way you can find out is your daughter allergic to something or not is to consult with your doctor. Since she is a teenager I believe that it would be best to visit her pediatrician and if he thinks that this is case for ophthalmologist he will recommend you to see him.
But this could be some kind of infection as well but since you have used warm compress and swelling didn’t went down try to explain to your daughter to avoid touching that eye. Keep us posted about her condition.