There is a Medical Centre in Incheon Int'l Airport which is run by INHA University Hospital.
This is the English web page of Incheon Int'l Airport
http://www.airport.or.kr/eng/airport/
This is the Medical Centre:
http://www.airport.or.kr/airport/facility/efalicityInfo.iia?carId=34
Category : Inha University Hospital
Items : Hospital/ Dental clinic
Hours of Operation : Always Open
Location : 1B, East Area
Tel : 82-32-743-3119
The hospital provides emergency treatment in case of the patient occurrence in passenger terminal, cargo terminal, CIQ area and inside of airplane for the passenger’s health care. It also checks weak passenger’s ability to fly and issues the internationally certified medical diagnostic statement.
link:
This is the Pharmacy:
http://www.airport.or.kr/airport/facility/efalicityInfo.iia?carId=35&fake=1177102912713
Category : Sam Il Pharmacy
Items : Medicine, Red ginseng, Korean traditional medicine, Health assistance foods
Hours of Operation : 07:00 ~ 20:30
Location : 1B, East Area
Tel : 82-32-743-3399
For the convenience of travelers and personnels residing in Incheon international airport, we prepare prescription medicine of airport medical center Inha university and sell Ginseng Red, neutraceuticals, non-prescription drugs and OTCs at moderate price.
You may lodge your complaint to the site directly.
Goto Customer Center, and register as a member and leave your complaints/comments/inconvenience to the Customer Suggestions section.
They said they would reply to you within 24 hours.
Here are some guidelines for you when asking question:
http://www.airport.or.kr/helpdesk/bul/bulInfo.iia?langGubun=E&fake=1177103619572
Leave your comments to the Customer Suggestions (icon on the left column):
http://www.airport.or.kr/login/FLogin.iia?ret_url=%2Feng%2Fhelpdesk%2Fpropose%2FProposeMain.iia
P.S. The staff l met in Incheon Int'l Airport were quite good and Korean people are quite helpful. Wonder who did you talk to because it seems to me that usually Korean people do not speak very good English and they might not understand "1st aid", "band-aid" "sterizing" etc... At that time you transferred at Incheon Intl Airport which means you were at the restricted area. May be you talked to a flight attendant or airline staff who did not know Incheon Intl Airport very well. The officers at the airport may not be found in that area. Immigration officers are at the immigration counters.