If you want to purchase regular non-prescription drugs for things like colds, digestion problems, or fevers, you still need to go to a pharmacy as pharmaceutical products are not sold in stores. Pharmacies sell mostly only pharmaceuticals but sometimes also sell cosmetic products as well. Also, since pharmacists cannot fill prescriptions without a prescription from a doctor, you should first go to a doctor if you think your cold or other sickness is serious enough to need more than a drug sold over the counter.
There are also many individual clinics (for internal medicine, surgery, dentistry, gynecology, otolaryngology, dermatology, urology, etc.), as well as many hospitals and clinics specializing in oriental medicine.
Most medical examinations and prescription pharmaceuticals are covered by medical insurance. Getting either is far more expensive if you do not have insurance, so a foreigner intending to stay in Korea for a long period of time should get medical insurance. Foreign citizens are not required to have medical insurance, but can apply for it if so desired by submitting to National Health Insurance Corporation the documents such as a copy of their alien registration card and documentaion on their purpose of stay in the country.