I would take it to Apple for either an in warranty replacement if you have Apple Care +, or an out of warranty repair.
Many places advertise replacing the glass, but you never know what you are getting. I had an iPhone 4 with cracked glass, and I was just using it as an iPod. I decided to send it to someone from ebay with a good rating, and have it replaced. The device worked PERFECT when I sent it to them, just had a crack where I swiped my finger to unlock.
They advertised quick turnaround, took two weeks. Came back and the phone would NOT even power on, unless plugged in to AC. As soon as cable was removed, it died. Sent it back to them, came back the same way again. Now without device for over a month.
They then refunded the repair cost, and I was left with a brick. Since they refunded my money, I could not even leave bad feedback. I just lost a perfectly working device.
I learned my lesson. Just FYI. Had this been my Phone I use every day, it would have been disastrous. I sold the phone for parts, and purchased an iPod Touch.
Just my 2 cents!
