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.
if the underwear is dry and hasn't been worn the same day YOU want to wear it, then no...you CAN catch something-IF-the person who has an STD, got fluid on the underwear, it's STILL wet and then YOU wear it... if the underwear is dry, the STD germs are DEAD. (they can't live without moisture).