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.
STDs and penile rash. Organisms that can be transmitted sexually (scabies, pubic lice, syphilis, herpes viruses, etc) can also produce rashes on the penis. Scabies is caused by mites that burrow into the skin.