Sadie made it through the night, and she seems to be doing okay. While she definitely has something going on in her lungs, I think being nervous at the vet exacerbated the issue. We'll take her back in a week for another X-ray. If she seems to be improving, we'll consider getting a CT scan done. That would be able to tell us more about the underlying issues.
Thanks for all your prayers and well-wishes. It helped get us through the night.