So, my iPhone 5 screen cracked.

Today, my family and I took my stepmom out to dinner. When we left the restaurant, I was using my phone and one of the staff bumped into me on my way out. The iPhone slipped out of my hand and landed on the concrete, shattering the front screen.

I normally keep my iPhone in a case, but I had taken the phone out earlier in the day to clean the phone and the case (the seams collect cruft over time). I didn't realize that we were running behind, and rushed out the door, forgetting to put my phone back in its case.

I'm posting here because I've only had my iPhone 5 since April 26, and I have insurance with AT&T. The nearest Apple store is about an hour and a half away, while the nearest AT&T store is about 10 minutes away, and the store I bought the phone at is about 40 minutes away. I've read around and the prevailing suggestion is to go to the Apple Store (since I haven't had the phone for a month). What I want to ask is, seeing as how I've only had the phone for three weeks, what are my chances? I've never taken anything to an Apple store to be replaced, despite this being my third Apple device.

My main question, TL;DR: am I better off going to the Apple Store first and seeing if they're willing to give me a full replacement, or should I just go ahead and work with AT&T, since I have insurance?

Any suggestions would be helpful.