I suddenly just stopped receiving text messages, saying my messages are too full...I deleted lots and reset it and I'm still not receiving any...help?

Okay, just randomly an hour ago, I received a message saying "Your SMS mailbox is full. New messages cannot be received until you delete some messages." So I deleted almost all my messages...didn't help. Turned it off many times, didn't work. Reset all my settings and plugged in my phone to iTunes, still am not getting messages. I've tried everything and the message still pops up. Help? I know I'll probably have to call my cell provider for support but I just want to know if anyone else has gone through this.