Try clearing the cache on any apps that send files or photos, I have this problem I'm using textra & it seems to be an issue after I've sent a photo. I think there is some kind of network hangup going on because all of the solutions people are suggesting tend to reset or clear the mobile network settings. So try clearing you cache for apps like text, FB, Twitter, Snapchat or anything else you might use to send files over your mobile network. see if that works. I would suggest clearing the cache of each app one at a time then try turning on your wifi after each one so you can locate which one is causing the hangup.
Goodluck!