Hit by a car in Korea: what to do first

Call 119 before anything else, and do not settle at the scene. A police report is what makes the driver's insurance pay.

Right now

Call both 119 and 112. Reporting to police is required when anyone is injured.
Don't say you are fine and walk away. Pain often shows up hours later.
Get the driver's name, phone number, plate number and insurer, and photograph the plate.
Note witness contacts and where dashcams or CCTV might have seen it.

See a doctor and get a medical certificate even if you feel fine. The first record is what later claims rest on.
Ask the driver to file an injury claim and give you the claim number, then use it at the hospital.
A traffic accident certificate is only issued for accidents reported to police.
If the driver fled or had no insurance, the government compensation program for motor accidents can cover you.