In the video for "I'm a princess," there is an almost-constant border around part or all of the scenes. Some things, such as a few lyrics, the dream falling from the ceiling, the "what an interesting song" part where the guy is spinning on the bracket, etc., are not confined to the border. The thickness of the border, as well as its color, also changes throughout the video. Then when the video of you starts to play, it seems like you are referring to the border around you as a door, and these doors start doing some really interesting things and at some points there are many doors on screen, and even doors within doors. At 2:57 you can even see one of these doors forming around two other doors of you playing music. Then at 3:13, all of the scene with the set (really the whole video so far) goes through ANOTHER door (this time an actual door) and into your room, which has no borderdoor around it until the ceiling "goes."  This seems super intentional but I'm not quite sure what the border/door signifies in the context of this songvideo. My initial theory is that the border represents a view into a dream, and that whatever escapes that dream view is somehow escaping the dreamscape. But, like I said, I'm not sure.
it represents "i'm in way over my head and i have no idea how to finish this video in my lifetime and make it actually the way i want it, so i'm fucked. and i just realized borders make most things look better, so that is somewhat of a liferaft for me in this situation"