I had root canal

It is always better to have the original dentist re-cement the crown. Unless you are going back to India shortly, you will need to visit a local dentist to do this.

I am concerned as to the reason for the crown loosening so soon . This will need to be ascertained. You may find that the treatment as a whole may need to revised before re-cementing the crown (if it is indeed possible to do so)

The fee ,to re-cement a crown ,for a person who I treat regularly may be £35- £60 as I would have a record of the history of the tooth as well as the persons mouth as a whole. The fee for the situation you describe may therefore be subject to an initial assessment and X-ray.
 

If your treatment was needed in India, you will have to view your treatment as a part treatment and have it resolved locally and so paying for the adjustment needed. You will be lucky to get a local dentist to take responsibility for this product. When a crown is made it is made for an ever changing oral environment. A dentist includes in his cost the initial care of the product and takes on the responsibility adjustment and upkeep within reason.
This is a good reason to stay local for treatment. If you are ever abroad and need treatment it would therefore be better to have the pain addressed and aim to have your full treatment where you can commute to easily.

My normal fee for re-cementing a crown is between £35 and £50 for regular patients where I know the history of the teeth. If you do not have a regular dentist then it may be necessary to take x-rays and examine your mouth as a whole to understand WHY this crown has failed.
You do not state if this is a temporary or permanent crown.
If it is temporary then it is easy to refit and have the treatment completed by your local dentist to provide a permanent crown once you know that the root filling has been successful.
If it is permanent then I would have concerns that there is a problem, with the tooth or fit of the crown, as it should not come loose in such a short period of time. This may be a sign that additional treatment will be required rather than just re-cementing as you suggest