How to recover photos from a destroyed iPhone?

Okay, so I dropped my phone and my whole screen is unresponsive. We went to the apple store and they couldn't repair the screen due to water underneath. I've gotten a new iPhone 6 from my carrier's store. I have nothing backed up, I don't use iCloud. Is there no hope in getting these back?

This is where you have a good lesson learned on why you do backups.