OK, so it really wasn't that dramatic. So I went through one of those cheapo carwashes (yes, I know they can scratch the car, but it was one connected to an Irving where you can get a discount on gas if you're getting the car washed, and my car was filthy

), and when the car came out, the weather-proofing strips that run between the front and back windows had popped off on both sides and were hanging off.
Turns out they just hook in and aren't glued. I reattached them, but then called the dealership just to be sure glue hadn't dried up or something.
And now that I'm writing this, I'm having deja vu about it. I think this may have happened to me a long time ago too.
So I guess the moral of the story is wash cars yourself, lol.