I read this story probably ~15-20 years ago - I don't know if the story is much older. I believe the story is in the form of a novel and not a short story, but I'm not 100% sure. The plot details I can remember are:
There are immortal people who can turn into dragons.
The protagonist was one of them.
The protagonist wasn't really a "good" person. I think none of these "species" are "good".
An antagonist (can't remember if it was the main antagonist) was also one of them.
The protagonist "kills" this antagonist by ripping his body apart into many pieces. I think even then the antagonist isn't "dead", but just neutralized (he's immortal after all).
The protagonist has been around for ~thousands of years (not 100% sure on exactly how long, but I do recall it was a long time - longer than a normal human lifetime at least).
The protagonist may have longed for death.
I think it was a story directed at young adults. I was really into Dragon-Lance at the time so I probably read this story expecting a similar kind of experience. -- MIGHT BE FALSE
Pretty sure the events of the story happens in a (my impression is modern) city - not a rural area - but I can't remember which city (or if it was really modern).
The protagonist is more senior (older) than the antagonist.
I think the members of this species might all serve some much more ancient/powerful being but I don't remember any specifics on that.
I'm pretty sure the cover was dark and featured a dragon.
I think the novel was pretty explicit now that I'm thinking more...perhaps with explicit sex scenes or explicit violence and gore. This would suggest the novel is NOT for young adults...but I really can't remember unfortunately...
That's as many details as I can remember right now. If I think of more, I'll update.