Sounds like your carrier settings might have gotten messed up. Try shutting down, taking the SIM card and and restarting. Then shut down again, put the SIM card back in and restart. Hopefully, the phone will reset the carrier settings.
If you are using Hangouts as your SMS app, you also need to check the APN settings within the app as well and make sure they are set to the correct APN. This seems redundant and should not be necessary but there it is, good luck.