When you launch the Avast app on the phone do you have a yellow button at the top with the word “Issues!”?
If so tap it and try and rectify them.
Do you have any other ‘sms apps’ on your phone? SMS backup, SMS forwarding, SMS emiticon apps or anything similar installed? If so they could be interfering.
If all else has failed with you installing non-root then installing in root mode maybe you could benefit from completely removing the app and try to re-install in root mode. Use the uninstall wizard by launching the avast app.