It's not really apocalyptic fiction, more like a deep-thinking introvert trying to survive an anarchic environment after a catastrophe (not nuclear) that caused half of a town's residents to flee. Won't have any zombies, just alive man against alive man and alive man against nature. I want to make it as meaningful and non-cliche as possible, expressing themes of the advantages and disadvantages of introvert personalities as well as the good and bad of anarchy. How should I go on about writing the short story? What should I avoid, what sensory details should I use, etc.
It's hard to give advice without knowing more about the world you've envisioned. So far all we know is that one town evacuated 50% of its population because of a non-nuclear catastrophe that did not result in zombies and your protagonist is an introvert.
Yeah, more detail would be good. But I could give you some basic thoughts. Apocalypses aren't just about the dramatic aspect of it; the danger. Depict normality but affected by the situation. It would be good at the same time to have a theme of "some things never change" because it's realistic and meaningful. If the town is the only affected place, you'll need an explanation why help doesn't come. Don't portray the idea of everyone being a worse person now. There would be complexity to responses that that. Don't kill your protagonist just to make it gritty, it needs to serve a practical plot purpose or send a strong message you want. Avoid familiar survivor groups; the nice underdogs, the survivalist rulers, the free neutral etc, unless you do them in an unfamiliar way. Don't portray society as losing order. Humans are social, organised, and thought-based creatures, society is an instinct as much as hunger. Even the antisocial usually like to have friends or something. Come up with a believable explanation for the apocalypse that would sufficiently delay or prevent attempts to rebuild. Especially useful would be negative psychological elements of consequences, like some denomination or group of a controversial nature, perhaps with a bigotry against it?The conflict could keep society down to a lower level. That's about all I've got other than write an non-simplistic plot with non-simplistic characters, probably quite complex if you want realism and meaning.
To be clear; it's okay to do cliches, as long as you take them more creatively, add more creative layers, or surround them with more creative stuff. Don't worry at all about tropes. Pretty much everything's a trope. http://tvtropes.org/
And just generally don't get caught up on originality that much. It's quite good, but there's also realism and practicality to consider. Some things just work and are worth considering.