I'm not a fan of rhyming, but it sort of worked here. However, the thought doesn't flow right from beginning to end. There is a place and a time for one-sentence poems, but this is not it. It winds up too much as a run-on...
Here:
I'm dying a slow painful death.
With each last ragged breath,
my heartbeat fades in my {chest}.
Now only a hollow shell is left.
Or, you could eliminate all punctuation, and insert some line breaks. I think that with the rhyme, line breaks could be interesting.
I'm dying a slow painful death
with each last ragged breath
my heartbeat fades in my {chest}
now only a hollow shell is left
Also... as a matter of personal opinion and nothing more, I'd eliminate the rhyme from the last line. But that's just me.