Use the free GarageBand app on your iPhone to turn your sound file into a ringtone.
Once converted, go to Settings > Sounds & Haptics > Text Tone to assign the new sound to messages. Iphone Sound Free
You can also download specialized, free apps like Text Message Sounds from the App Store. Use the free GarageBand app on your iPhone
If you want to use these downloaded sounds as custom text tones or ringtones, you can do so for free: Download: Save your chosen sound file to your Files app. Iphone Sound Free