I think any hospital  can test and treat you for that. Many Koreans catch an STD . However not sure what infection the person mentioned. I think you must get a test with your id card or passport you can not test without a name. In the States or many countries you can test without giving your ever detail.

In case someone test positive for hiv  you are deported .Korea still lives in the stone ages when it comes to Hiv prevention. Some feel if they sleep with a Korean hooker no need to wear a condon. Well not true hiv is found in every country and sex workers have it the most. Korea may not have as much hiv as western countries but they have just as much or more of STDs,   genital warts  or uninary track infection transmitted my sex.

Not to sound like your father  or minister or priest   the best way to prevent it  is to wear a condom or just abstain for sex. All teachers have been tested for hiv however all most no Koreans have been tested. You are clean but others may not be. Dont risk your life for an hour or so of fun . Wear your raincoat  Dying of hiv is a long and lonely death  unless you have alot of money to buy medicine.