Was stumped until I realized the game is glitched.
 

I picked up the bottle in the cell at the beginning, but after going through the cut scene afterwards it disappeared from my inventory. I didn't think much of it until I got stuck shortly after trying to find a "container" for a drink for the bum.

It's a shame I'll have to restart the game again hoping that this doesn't happen again.
Here's hoping for a patch!

I didn't come across that glitch, but I did come across the glitch that allowed you to do the "Menage a Moi" quest TWICE (except you couldn't give the spare doll away, so it stays in your inventory until the end of the game).

This is what people in the industry refer to as "swag".

The same thing happened to me. I lose the bottle from my inventory. Did you sort it out?