Not receiving Text Messages after upgrade to iOS 7
I had something similar. To fix it, go to the Settings app, then General, then scroll down all the way to the bottom and tap Reset. 



This gives you various choices, but Reset Network Settings is what you want: 



you will then be given a confirmation to Reset Network Settings -- tap the text. 



The phone will restart, and your Messages and texts should work fine. You may have to enter your WiFi passwords again, and on my phone, Mobile/Cellular, the toggle for Mobile Data / Cellular Data had been changed, so it may be an idea to check that.