This story initially came to my attention as a piece on Fox News and so I decided to dig a little deeper. The story seemed initially to be a little suspect as it was missing a reliable source and could potentially be pushing a false narrative.
After a brief fact check it became apparent that the original story (published by two Associated Press journalists) from which all other iterations had been derived, depended almost entirely on contact with an unnamed doctor working directly with the Iranian health ministry.
While this does not rule it untrue, it does make it somewhat questionable, as the Iranian government is vigorously opposed to alcohol use and regularly makes a point of vilifying its use.
Furthermore, methanol poisoning from bootleg alcohol is responsible for the deaths of dozens of Iranians every year. This is due to restrictions and the resulting black market and poor manufacturing processes.
I was unable to locate any reference to who, if anyone, was pushing the claim that alcohol treated the Corona Virus inside Iran.
Given the volume of deaths and hospitalisations quoted in the AP article and the fact that the story has precedent (although unassociated with the Corona pandemic), it would not be a stretch to assume that alcohol use had risen in recent weeks and months and that hospitalisations and deaths had increased as a result.
However given the lack of information on who is claiming alcohol is a cure and the questionable motivations and identity of the AP source, the truth of this story remains uncertain.