"I just don't know where we stand"

From what I can tell yes you two definitely have a relationship. Not all relationships have to be the typical "will you be my girlfriend, let's put it on facebook" type of relationship. As long as you two are both on the same page, and it seems like you are then not having it out in the open for all to see or know isn't such a bad thing. Sometimes the reasons relationships don't work out is because other people get involved. So yes in my opinion you two are definitely in a relationship,so congratulations ! Don't worry, it's completely normal for people, especially girls to question the status of a relationship, and sometimes it's uncomfortable to ask the other person where you stand without making things too awkward.