There are quite a few threads on this topic, and I know some people reported back pain, but most of the threads are about the opposite effect that unicycling HELPS with back problems:
Unicycling helping my back pain
If you already have major back pain and inflamation, than I don’t think it would be good, but otherwise it’s usually positive.
Maybe check your setup and how you’re sitting, maybe crouched too far forward? Sitting upright as unicycling encourages is great for your back, as well as the movement to exchange fluid in the discs and strengthen the muscles.