Ouch. That sounds painful.
My suggestions, based on dealing with upper back pain from my scoliosis:
1. Stretching. Yes, do core work, but pay attention to hamstrings. The hamstrings in cyclists tend to be tight, which can lead to lower back pain.
2. Preload with Ibuprofen.
3. Get a bike fit.
4. Pay attention to proper posture on and off the bike. I don't know what structural problems you may or may not have, but if you have any, take care of time off the bike. I can tell when I'm riding if I've been spending too much time in a scoliotic slouch off the bike, simply based on how my back feels when riding.
5. If it's a muscle problem, a little rest will reduce the pain, although you will suffer some stiffness. If your problem is in a joint or bone, then you should see a medical professional.