The distinction between organic and inorganic carbon compounds, while useful in organizing the vast subject of chemistry... is somewhat arbitrary. Organic chemistry is the science concerned with all aspects of organic compounds. Organic synthesis is the methodology of their preparation.
No, it is not possible to contract the typical STDs, such as syphilis, gonorrhea, chlamydia, hepatitis B, etc. from wearing someone else's dirty underwear. However crabs and scabies, may be spread in this fashion.
There are various sexually transmitted diseases that can infect you because of risky sexual intercourse including HIV, syphilis, gonorrhea, herpes, trichomonas and HPV. The type of test and also the type of disease that you are taking a test for determines how long does STD testing take. Some of these do have pathological tests to detect whereas some do not have. The common symptoms are irritation in the genitals, soreness, pain while urinating and discharge from genitals.