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.
Education of children and teens is vitally important to help prevent sexual transmission of HIV, as well as other sexually transmitted diseases (STDs), including chlamydia, genital herpes, gonorrhea, hepatitis B, syphilis, and HPV (which can cause genital warts or lead to various cancers).