That is interesting to be so totally into a dream that you don't know your own identity. I can't say I've experienced that, maybe. But I have had lucid dreams so real that I could use all my senses, and it was very convincing. However, even in my lucid dreams, there is something 'unreal' in the settings. The backgrounds generally look like scenes from 'Contact'. That's my best clue to knowing I'm in a dream.
I think in your sitaution the best thing is to stay calm and just go with it. Don't worry too much, and keep looking around at everything, you never know what you'll find.