I am from Nepal and I bought an iPhone6 around a month ago. The bottom right corner of the screen is already loose. I just can't find a way out what can be done from here

iPhone warranty is not International, you need to bring it back to the place you bought it for warranty services.

Then buy the phone in the country you intend to use it in and you won't have that problem next time. Don't blame Apple for your mistake.

I am very sorry to hear about your problem. I hope you will get it fixed soon.

Hey can you help me with other info. Do NTC provide nano sim for iPhone 6? or Is there any other way to make existing sim work for iPhone 6, like those street side vendors use to cut sim to make it micro, Do they do that for nano too? It would be very helpful. Thanks

See if the Pentalobe screws at the bottom are loose or missing. Might need to get a special screwdriver from iFixIt to tighten. Warranty will be voided if you open it, but just tightening it up won't cause a problem provided you don't strip the screws.

if you are disappointed with apple tell them using feedback

https://www.apple.com/feedback/iphone.html

telling other users in a user helping user forum is pointless