Can Apple fix my unresponsive screen?

I dropped my iPhone 5S and there are white vertical lines on the right side. The touch has stopped working, so I can't unlock my phone. The screen isn't cracked, it's just unresponsive. If I take my phone to the Apple store will they be able to fix this? I don't want to have to get a new phone or have mine be restored, I just want to know if there's any way they can save my phone so I don't lose everything.

They can easily fix it but they will restore it, they follow a set of rules and one of them is to restore the device. You can create a backup via iTunes by plugging in your device on your computer

Maybe, but if it has alot of damage then they just give you a new refurbished phone instead.