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.
Sexually Transmitted Diseases (STD), also known as Sexually Transmitted Infections (STI) or venereal diseases (VD) are diseases that are contracted by humans through sexual behavior and activities. You cannot exactly differentiate between HIV (Human Immunodeficiency Virus) and STDs as HIV is a type of STD.