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.
Anyone who is sexually active risks exposure to a sexually transmitted infection to some degree. Factors that may increase that risk include: Having unprotected sex. Vaginal or anal penetration by an infected partner who isn't wearing a latex condom significantly increases the risk of getting an STI.