Well, as all other softwares the iOS 7 is also getting some stock app breaks! Its iMessage this time and seems like many of the users are messed up with the iMessage app after their upgrade to iOS.
So, if there is a problem we need to search for the solution. And here is one, not very big!
Just try to turn of the iMessage and turn it on again. For this you may need to
>go to the settings page and then turn off iMessage.
>go to General, then Reset, and Reset Network Settings.
> turn iMessage back on.
Okay, if this workaround is not working for you, what should be done? I do not like to say this as an answer but likely you will have to wait for Apple to officially acknowledge the problem give a proper fix.