You get HIV from having unprotected vaginal or anal sex or sharing IV drug needles. Having a bleeding hang nail in a public place won't give you HIV. It's a sexually transmitted disease. Transmission takes place inside the body and the virus is inactivated by air and saliva. Can't get it from a surface or from a transfer to a small superficial cut like a hang nail. So, absolutely no risk from living your life with a hang nail for getting hiv.