I had gone to the dentist for doing crown on 36th tooth. He took the x-ray and told me that there is cavity in tooth number 37 and so it is better to do root canal for the 37th tooth and thereafter do crown job for both teeth numbers 36 and 37. He said that there will be pain for about 2 days and to meet him after a week. But the pain persisted for more than 2 days and there was also a slight bad smell. After I met my dentist, he once again drilled tooth number 37 and again prescribed pain killers and asked me to consume pain killer medicine for 2 days. Now it is the 3rd day. I get terrible pain, if by mistake, I chew even soft foods like banana. In the night also I get terrible pain if I grind the tooth in deep sleep. Terrible pain means that I virtually see stars. The pain is there even though I take powerful pain killers.

It sounds like there is still a nerve in the tooth. If the root canal has been done right you should have no pain whatsoever. Perhaps it is a different tooth that is causing the discomfort? I'd suggest you go for a second opinion.

The tooth 37 must have had a very large area of decay for it to need a root canal. Was there no sensitivity before the root canal was started?

The decay in tooth in tooth number 37 is only a small area adjoining the tooth number 36. Before doing root canal, there was no pain. The pain started only after the root canal procedure was done. Only temporary filling has been done. It seems that the permanent filling will be done only if there is no pain. Originally after the root canal procedure, I experienced pain only when chewing. Now the pain has increased and is present even when I am not chewing. Originally the pain medicine had effect for at least 8 hours. Now it is effective only for about 4 hours.

You really need to get a second opinion. I see no reason for the root canal being done on tooth 37 in the first place. I'd recommend you see an endodontist, a root canal specialist.

For getting 2nd opinion, I met an endodontist. He saw the case files and asked me to take an X-ray. He saw the x-ray and said it seemed OK. Then he said that he will remove the temporary filling to see if there is any infection. After removing the filling, he said that there was a slight infection and he had removed it and then applied medication and once again did the temporary filling. He prescribed new pain killer medicines and one morphine like drug which he said I had to take in case the pain killer medicine did not have any effect. He told me that if pain persists, then there is no other option except to have the tooth extracted. The new pain killer medicine is also effective only for 4 hours. Is the problem with the tooth or is it something to do with the nerves from the brain? How to find out the difference?

Has the dentist checked the bite? When you close your mouth gently does it feel like the teeth on the side with the 36 and 37 meet first? If it does, you should have the dentist adjust your bite. Did either dentist prescribe an antibiotic at all?

With this much pain ,you could go to the emergency room and get this looked at.
I would call your DDS first and tell him what you are experiencing, Dry tooth socket seems to fit your symptoms.

It is quite common after tooth extraction.

This could be an instance of dry tooth socket and it needs to be addressed .

Here is a link that I hope you find helpful.

Dry socket - MayoClinic.com

There has been no mention of an extraction having been done yet, hence it is not a dry socket.