My iPhone 5 sound will not work!

I will only have sound when on speaker phone or when the headphones are plugged in. I have tried to restart the phone and plug it into itunes with no luck. Will still vibrate and says that the ringer is in (headphones) but they are not plugged into the phone. There is absolutely no sound that outwardly comes from my phone EXCEPT when I go to Settings > Sounds > Ringtone. BUT ONLY RINGTONE! If I try it with anything else, text, voicemail, tweet, ect, it will only vibrate. I have only had my phone 2 days!