Are you interested in medical tourism in Korea, or you are looking for a doctor?
Try the Gangnam Medical Tourism Center. They have an English language site available to help you search for English-speaking doctors.
I’ve used it a time for looking for an oriental medicine doctor (also known as Korean traditional medicine). It was successful … as for the medicine? That’s a tale for another day! Successful? Yes. Long-lasting? Nope… ^^;
Here’s a picture of the main site.