I remember reading this manga a while ago and when I went back to read it again, I couldn't remember what it was called.
I do remember in the first or second chapter that when he came to that world, he woke up on top of a tall building. When he woke up, he ended up seeing another girl jumping to her death to get away from a man in a butcher outfit wearing a mask on another building. The butcher soon started to chase after the main character, so the boy starts to run across bridges to get to other buildings where he soon finds the gun that ends up having what seemed to be the parasite in it. With the gun, I think he ends up killing the butcher and later finds the girl and dog. I also remember in one of the last chapters, he ends up fighting a person in a bunny mask and dress with the girl and dog on his side.
The main character had black hair and seemed to be quite young. The girl also had what looked like long black hair and looked to be even younger than the boy. The dog also looked like a small Shiba Inu breed. The parasite that he ends up getting looked like a black blob with an eye.