First, remove the disclaimer - telling the reader there's not going to be any logic is a bad way to start.
More description of the setting - not in painstaking details, but some colors and smells and feelings beyond pain and fear. Right now, it feels like the characters are actors at a dress rehearsal where the set designers have only gotten the layout complete and are still working on backdrops and props. They're in costume, they know their lines, but have nothing (but each other) to interact with. Some playwrights can get away with this (Harold Pinter, for example, or Samuel Becket who made a point of minimalist set design, making it almost a character itself), but not a novelist.
It might help to try to rewrite the scene in third person, look at what works and what doesn't, and then either revise it to BE third person, or to incorporate what you discovered in shifting perspective. One example to follow with this would be Peter David's Howling Mad - the chapters shift between two characters - sometimes in first person, sometimes in third person limited. Like describing a scene where the heroine comes home to find a wolf in her kitchen. The wolf immediately walks up to her and sniffs her crotch. The next chapter is from his POV and is simply: "It seemed the polite thing to do" - and the next chapter is from her POV.
And I can see what DismalNaim meant with the first chapter after the introduction (The Cave) - spacing issues, some places that need commas, some clumsy wording; feels like a bad translation at times. Much harder to get through than the part called Ch1: Beginning After the End - plus no explanation of how the characters got there. This could be a better opening than the first if it were put together well. Describe the fight, and then have a "record scratch" moment where the narrator realizes the audience has no clue what is going on and rewinds to earlier in the narrative to provide those details before resuming the adventure. COULD be... but, instead, it feels more like a dead end.