iPhone screen won't respond to touch!

Last night randomly my iPhone 5 screen just wouldn't resond to me. I couldn't unlock it, it was acting like I wasn't even touching it! Every now and then it would let me unlock it but then it wouldn't let me do anything. All my buttons work but not my screen. I restarted my phone, didn't help. I restored my phone, didn't help. I don't have an apple store anywhere near me, I don't know what to do. My phone is still under warranty, so is it possible to get my phone traded out?