I added a few MP3's from a site http://www.freesfx.co.uk/sfx
They only work as ringtones but will not work as notifications. I have the three folders- Ringtones, Notifications and Sounds, but there is no choice to "set as" notification" only Phone ringtone, Caller ringtone or Alarm tone. When I go thru settings/sound settings/notification ringtone they do show on the list, but even when chosen they do not play when I get a text message. I have also tried restarting. No luck.
I don't know which phone you have, so these steps may be slightly different depending on your phone. Open your text message app, then try menu > settings and then look for a notification ringtone option. Choose the ringtone you want and then it should ring whenever you have a text message. If you've just been changing the notification ringer under Sound, that just changes the way notifications sound (like letting you know that the phone is fully charged).