iPhone 6 dropped on my sink no cracks but broken inside
Ouch! There's two ways you can possibly save your phone here.

Accidental damage is covered under AppleCare+, which is a separate purchase. If you don't know you have this, you probably don't. 

(But try calling Apple support at 800-275-2273 and give them the serial number)

You may also have insurance through your carrier (commonly called Asurion, TEC, or something else similar), if you have this, it's a separate line item on your phone bill.

If not, I'm afraid you're out of luck :(