LTE & 4G not working on iPhone 5?

My LTE and 4G never works and I just got the phone last month! I try to go on the Internet but it won't let me and I have it unlimited. What's the problem? It only works on wifi. My iPhone is up to date with its software and I went to the setting and then cellular and made sure everything is on but it still won't work! I can refresh my emails and can't check my social media sites. Does anyone else have the same problem? Should I take my phone back to AT&T? What can I do to fix it? Thanks!

You cant get "Unlimited LTE" on AT&T and then i recommend that you check your coverage and see if you are in a 4G LTE service area att doesnt have much lte coverage though Verizon covers most of the US With 4G LTE and if you are suppost to get lte in your area then bring your phone to AT&T