I'm in the notification control screen, everything seems to be turned on, yet, when I receive a text, there is no sound alerting me that I've received the text message.
First, make sure you do not have the phone in Mute mode (switch above the volume buttons). Make sure you don't have the phone in Do Not Disturb mode (there'd be a crescent moon by the battery icon at the top right of the phone), ensure that you have sounds enabled for texts, and notifications turned on for texts.