Hey Dan,
Hopefully this note gets to you before you go to a mechanic. That loud buzzing noise that occurs after the headlight goes down..... does it go on for about 5 to 10 seconds? Also, has it started making the same noise when you arm your alarm? Sometimes even with the lights briefly popping up and then down again?
It's more than likely the plastic toothed cog gear in the motor assembly that raises and lowers the light. GM, in it's unwise wisdom, engineered those things with plastic instead of metal, guaranteeing their failure sometime in the future.
That noise you are hearing is the gearing grinding and popping against it's opposing metal part. The teeth have worn down to the point where it is doing that. Sounds almost like a mini-jackhammer.
The motors almost never die and the electronic brain that controls the lights can go bad, but that is very rare as well. I had the same problem on my '98 T/A and I fixed it for $45 plus shipping. You take off the light's painted panel, unscrew the plastic facing to the headlight, disassemble the headlight from its housing and the motor, finally take the motor out (3 bolts only, first two are very easy, the third is a little bit of a pain). Pop the plastic lid off of the plastic gear housing and replace the gear with an aluminum or brass gear. Epoxy it back on, making sure the bond is a good one, and then put everything back in reverse order. I'm not very mechanically inclined, but I did it due to not wanting to spend $300 or $400 at the dealer..... and they do take you for a ride if they can.
OK, the metal gear I bought is $45 from Brent Franker in the Tampa Bay area. He's honest. Here's his website:
http://www.bfranker.badz28.com/headlightfix/index.htm#Ordering
Read the entire website, he diagnosis everything very well. I'm 98% sure, from the way you described the problem, that it is only your gear.
Brent even has a video link that shows you how to replace the gear. It isn't a super easy job, but it IS very doable for even a novice such as myself.
Good Luck,
Jopagering