Haha, wow VA, you're woman drama always amuses and makes for a good read. Girl B is kind of a pushy nut isn't she. You seem to be the type to not like to talk about others, which is cool; so I say don't acknowledge any type of relationship. It may suck that other people think you two are a couple, but I wouldn't go out of my way to tell anybody you're not, unless they ask. This way, you're still a nice guy, and people will eventually notice that it's a one sided relationship, and she'll look like the fool.
With Girl A, it seems as if she just likes the fact there are two guys that like her, and it makes for a better story, and she seems more wanted, if there's conflict between you and the other guy.