Here's my diagnosis of the question:
- It starts out by criticizing the simple line
He heard a cough behind him as "telling" rather than "showing." That's a criticism that can be justified, but it's relatively an extreme case to be concerned over. What OP means is that the line is factual, terse, and not particularly rooted in POV.
- As soon as he tries to improve it, he finds that a greater level of detail and POV focus force him into dealing with subtleties and nuances of phrasing. This is not longer a show/tell question; it's just that going into greater description increases room for that kind of nuance.
So I see multiple possible issues here:
- show vs. tell tradeoffs
- whether/when simple lines need to be converted to be more "show"-y
- once you're rephrasing the line, how to actually achieve the emphasis and immediacy OP wants.
1 and 2 are both potentially duplicates (but not necessarily); 3 may be a rephrasing question (but not necessarily).
I'd actually recommend OP splits this into 2 questions: one on whether such a short line needs to be toyed with at all; a second on their difficulties finding the right emphasis and immediacy. (The wider question of show/tell tradeoffs is a duplicate, unless OP has a specific facet of that they want answered.)