This vestibular syndrome is very common in elderly dogs. Occasionally, it is caused by an inner ear infection, occasionally by hypothyroidism, and very rarely, by a brain tumor. The typical one we see so often in old dogs is considered "idiopathic," or of unknown cause. In most cases of these, the dog improves quickly--anywhere from one day to two weeks. Usually, the side-to-side eye movements improve first. The worst I have ever seen took about 2 weeks. Occasionally, dogs keep a mild residual head tilt or mild imbalance when shaking the head. A few dogs have more than one episode.
As far as what to do goes........Most important is to make sure that she can eat and drink successfully. You may need to carry her outside--go slowly, so she doesn't try to right herself. Raise her food and water dishes or, if needed, hand feed her and give her water by a turkey baster. It doesn't hurt to have a thyroid profile done, especially since you mentioned muscle atrophy. If she improves on her own, that pretty much rules out a brain tumor.
I hope this helps. Let me know if you have any more questions.