Without getting into the details of whodunit...is the narrator reliable? Is the narrator pathological? Is the murderer one of the other three? I think this oversimplifies what you have created here. Maybe you didn't intend it, but you achieved a state of universal paranoia that will prevail in the world once the survivors emerge from the bunker.
This is an apocalypse. We've seen the movies, read the books. Danger lurks everywhere. Resources are scarce, violence pervasive. When the people leave the bunker they may separate from each other, in the illusion that they are escaping danger, but there is no escape from the new order of the world.
When you say the dead may be better off, you suggest that perhaps death is the only peace any of the survivors will ever know.
The living, on the other hand, we lived in constant fear, unsure whether we even wished to wake up from our sleep or join the corpses in the morgue
That says it all. Good job!
RE: [Short Story] - Fallout