Could a human die through a dream?
Not in the sense you're probably after no, not in any other sense either, not if you're healthy.
There are two ways ("in the real world") you could possibly suffer physical injury or death from a dream, but they're both unlikely long-shots.
- If you have a serious health condition to start with that could lead to a heart attack or similar as a result of stress or blood pressure it's conceivable you might have a heart attack or something, if the dream is stressful enough.
- If you react physically to dream stimuli (either because you sleepwalk or just happen to be at the edge of dreaming & waking) you could have some sort of accident that might be lethal.
I actually broke my ankle "through a dream", I was asleep on a grass bank in the park (nice sunny day), must have been just on the edge of dreaming & waking because I tried to dodge something coming at me in the dream, I stood up before I really woke up, the dream ground was flat, the real ground wasn't, so that first step was into thin air & the ankle twisted.
can a dream so horrifying that it indeed bursts your heart?
Sure, but only if you have a very serious pre existing heart condition in the first place.
Would such a psychochemical agent be a feasible creation or would it be too fallacious?
Ah now that's another question isn't it..
It's "too fallacious", the worst nightmare in the world won't kill anyone healthy by fear alone.
You want a "psychochemical agent that injects dreams in the receptors mind that cause hefty stress reactions, leading then to a heart attack and thus certain death" : which (in & of itself) isn't plausible.
For otherwise healthy individuals you'll need something to weaken the heart, to make it susceptible to heart attack in the first place (as well as the "dream agent"), which will need to be dosed very carefully to insure it doesn't do the job all on its own without the stress caused by the bad (trip) dreams.
But the thing is why fiddle around with a second detectable poison in the victims blood stream when simply upping the dose of the heart attack causing one does the trick without having to mess around with dose levels to get it just so for the bad dreams to be what actually triggers a heart attack?
A combination of mushrooms, acid & mescaline for the "trip" in combination with a malicious trip-director chased with large quantities of whatever they're selling as speed these days, adrenaline & digitalis can probably achieve more or less what you're after, but with that cocktail there's no need for the recipient to be asleep, in fact it's easier for the trip-director to turn it into a bad trip if they're not.
It's questionable with that cocktail if the "bad dreams" are the cause of death or just a bit of colorful mental torture preceding the onset of the lethal effects of the overdose from the second set of drugs.