What Dave12308 said. If your using a secondary SMS program you most likely haven't disabled the stock SMS notification. If you are only using the stock SMS program a factory reset may be in order.
Sent from the rocket in my pocket, my all powerful DROID BIONIC.
Not sure how to turn off the stock app but as for the text app its the one that was installed on the phone out of the box.
Will I loose any of my information?
You could try installing another SMS client. Like Handsent or Go SMS Pro. That may stop the notification.
When they talk about turning off the stock SMS app they're talking about an option.
Open the stock SMS app:
menu>message settings>uncheck notifications.
Stuff will be synced with Google. Like contacts and what not. But everything else will go away unless you back them up to your SD card.
Ok so I went in and turned off the factory installed sms program and it turned off the first notifications you can choose in setting but now the only sound I get for notifications is the droid one. So got rid of one but not the one I wanted to get rid of. Thank you all for your help. I hope we figure this out. I really don't want to have to factory reset unless I have no choice.
This sounds like a pretty good indicator that there is a second messaging app installed that's producing the unwanted notification. If you don't know which app that might be, you could try posting a list of installed apps and maybe someone can identify some likely suspects for you.
Regardless of what you try, I think a factory reset is a last resort, and I don't think you're at that point yet.