Does heroin kill brain cells?

Heroin by itself has near-zero toxicity, the real danger comes with the way of consumption : snorting will damage your nasal cavities, IV done with hazardous hygiene will lead to all kind of very unpleasant infections.

As long as you don’t overdose (which basically means that your body “forgets” to breathe), your brains cells should stay perfectly fine.

If you want to know more about Heroin and how it affects the nervous system, you can have a look at this (chapter Opiates)

I stand by the two prior responses, but must add, unless you are getting pharmaceutical heroin, which is made with stringent quality controls, one has no idea what other crap that street drugs are “cut” and/or adulterated with.  There are a litany of things that could be potentially neurotoxic.
Secondly, while pure opioids are not neuro- (or hepato- or nephrotoxic), being high as a kite a lot of the time will certainly impair one’s mental and emotional development as a person.
BTW, self-injecting of any substance puts one at risk from numerous infectious diseases.  IV heroin users tend to develop infectious endocarditis – an infection of the inner lining of the heart and its valves.  You don’t want that.