Hi Alex ~ Sorry for your pain! My first thought, as usual, is Psoas, second thought is Stronger Abs. Many dancers have tight psoas and it leads to a tilting tendency of the pelvis one way or the other (swayback or flattened lower back). One good stretch for this muscle at the front side of the low back, connecting spine, ribs, pelvis and thighs, is to lie at the side edge of a bed and let one leg hang down to the floor, keeping the low back flat on the bed. Some dancers are so flexible that you will need a higher surface to get a stretch, and if it still doesnt happen, you may need someone there to push your leg down while you keep the other knee up to your chest. You can also press the stretching leg up against your assistant and then relax and let them stretch it again. Releasing the psoas can change your pelvic posture and holding dramatically. Then of course, nice strong abs, engaged actively with awareness while you dance, will help protect your low back. But in order to develop them you need to find a good crunch that doesn't just make your psoas tighter. I recommend avoiding straightlegged situps, for starters. Often a good guideline to avoid psoas engagement and use the abs is to begin with the feet lifted to 90 degrees and do the crunches frome there.
But first, take it easy and let your body take the rest it seems to be asking for! Walking in nature sounds like a great idea. Maybe put some heat on it. Gentle yoga. Be nice. You'll be dancing again soon.