Check your local area for iPhone repair shops. The prices vary so it is your best bet to call and ask. Verizon doesn't actually repair broken screens and I'm not sure of how much Apple charges (check their website).
I would return it to Apple for repair. The layers are fused together and need to be replaced as a single unit and calibrated with great care for good operation of your phone. Good luck on your repairs.
Glad I looked at the link you provided. Although I don't have a current issue I noticed there was a battery replacement program for the iPhone 5 that is active. A few months before getting my 6 plus I went and had the battery in my 5 replaced. Now I know Apple will refund me for that.