The way the title reads, you don't want sound alerts for anything except incoming texts, which sounds like you want to turn off alerts for everything else. The body sounds like you need sound for incoming texts. Have you enabled notifications for this app? Which app are you using? Have you tried a third party app for sounds like Zedge to add sounds to this app? Are you receiving sound alerts for other notifications? Have you checked that your notification volume is on and set to a level that can be heard? What phone do you have? Have you checked the app settings to see if there is a way to set an alert tone? Is your default notification tone for your phone set to silent? Will the phone ring if you receive a call?
Will provide more information about what you've tried, where you've looked for a setting??