Can bacterial vaginosis cause a burning feeling in the oris and just beneath it?

I have been having a burning feeling inside the inner labia just under the . It sometimes looks a little red and sometimes it does not. I recently took Diflucan and that didn't help. Now I am noticing a slightly thick, milky discharge. I'm starting to wonder if it could be bacterial vaginosis. Would BV cause burning in the oral area without causing burning in and around the ?