My initial (see edit below) interpretation was that the "right-side-up" world was first moments after death, literally leaving the world behind. The...something...chasing after the character felt at first representative of not wanting them to move on. In retrospect, it felt a lot like Jacob's Ladder, but that might also be due to the street names from Silent Hill and how Jacob's Ladder influenced that series so much.
So getting to the "upside-down" world at first felt like ascension to a higher plane or something, but after finding my way back into the building, that changed. I remember feeling like it was part 1 - Escaping and part 2 - Confronting. I felt like the character had to return to his death to confront what he did and ultimately move on, whatever that entails.
The weirdest thing I thought after playing was wondering if the creature was trying to chase you away from the end, or into it,
May not have been the meaning you were going for, but that's what I took away from it.
EDIT: Something was niggling me, so I went back and watched the ending again, and suddenly noticed something that literally gave me goosebumps (and still is as I type)
It was a pregnancy test. Two lines. Holy crap. Wow. I'm going to try to go back and play it myself again so I can look around the last couple rooms some more. It looks like a murder/suicide love triangle maybe, but I obviously overlooked a lot of stuff when I played.