No, Aspirin is not banned in India. You can buy it quite literally from any medical shop or in any part of the country. Though the source of this confusion may be the reason that in dengue season, specifically, some states in the country and their health departments go out of their way to ask chemists not to sell Aspirin as freely or provide alternatives to that to patients because it has been seen that Aspirin can increase the risk of bleeding in dengue patients. That could be the only reason, but it's not a ban in any shape or form.
One of the major sources of confusion is the list of prohibited drugs that the government publishes from time to time. Upon seeing that some of the combination medications that contain Aspirin have been banned, people tend to think that Aspirin itself has been withdrawn/banned, whereas that is not the case.
Moreover, in the height of dengue epidemics, places such as Delhi frequently announce short-term orders that are directed at pharmacies prohibiting the sale of Aspirin unless a doctor’s prescription is provided. Nah, it is not because Aspirin is a danger, but just to make sure that no additional complications occur during the given period. After the onset of the dengue virus, these limits are generally removed, and the situation returns to its usual state. Plain and simple!
The Central Drugs Standard Control Organisation (CDSCO) and the Drugs Controller General of India (DCGI) are the major agencies responsible for the regulation of medicines in India. How they work is pretty simple actually, like, after identifying a drug that is unsafe or not approved properly, they issue a formal announcement (known as a gazette notification) to prohibit it in the entirety of the nation.
In addition to that, state health departments may also implement short-term limitations to ensure the safety of the public, such as halting the sale of specific medications during a dengue outbreak. Though you should not be alarmed or feel a certain way because such decisions aim to safeguard the entire community.