Why don't you call Apple and have them replace it through the mail? Its under warranty and there is something wrong with glass/LCD assembly. As long as it hasn't been dropped or experienced any other accidental damage, they should replace it for free. I wouldn't trust a carrier replacement except from Sprint. Surprisingly, Sprint is the only iPhone carrier Apple has authorized to replace iPhones under AppleCare. Verizon, AT&T, and T-Mobile are not meaning whatever AppleCare you have is gone.
I recommend calling Apple, that way you still have AppleCare when you need it unless you pay TMO for extended warranty on your phone bill. I've done it before, never had problems with the service.
When you call, Apple will offer 2 services:
1. Regular Replacement. You can either have Apple ship you a box to ship the phone back to them or you can come up with your own packaging. (I recommend the former) You then ship it back with the label Apple shipped you (or if you use your own packaging, take it to the parcel carrier (UPS, FedEx, etc) and you have to give them a number Apple provided). Apple will then take the iPhone back, run diagnostics (if needed) then ship you out a replacement. With me, it went FedEx Overnight Priority both ways going this route. I had a new phone in about a week.
2. Express Replacement. It costs $29 for this route (unless you have AppleCare+, in which its free). What happens is Apple places a hold on your account (most likely a credit card) for the full retail cost of the iPhone and charge the $29 (if applicable). They will then ship you out a phone, which will take 1-3 business days to arrive depending on what time it was ordered. You will have a certain amount of time to ship the original iPhone back before the hold becomes a charge.
I have done it both way. If you can, I'd recommend the express replacement.
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