Dash tweeter? That means you've got the Bose amp, which is your problem. They go bad. And if you find another on the used market and swap it, IT will eventually go, as well.
Best solution is to replace the stock head unit, along with an add-on harness that will allow you to install the aftermarket HU while retaining the chimes, Onstar if you use it, etc. PAC and Axxess make them, among others. If you want to retain steering wheel controls (volume, source, etc.), they do that, too.
Do a search on our forums for info about doing this (you're not the first person this has happened to, for sure).
Finally, if you really like to crank up the tunes, you'll prolly want to get an aftermarket amp, and install that, along with the HU. And if you do that, a speaker upgrade is in order.
See how many problems that little amp has caused?
If you're not ready to bite the bullet and replace everything, you can adjust your fade / balance to eliminate the bad channels (in mine, they would be 'scratchy' / distorted at low volume.)