I've had the iPhone 6s and for about a month?

So I've had my iPhone 6s for about a month and my battery started dying all fast all of a sudden. Can I get a new one?

Sure

A new what? Battery?

If the phone is faulty, you'd be given a refurbished one through Apple (if you bought it new, which you didn't bother to say).

You could check with an Apple Store about your claims & see what they could do

Most likely, that sounds odd though as I haven't heard that happening to anyone.

As long as you haven't gotten it wet, a defective battery is rare, but can happen. That's what warranties are for. Take it in, let them check it and they'll replace it as long as you haven't violated any warranty requirements. (drowned it, destroyed it, etc)