The low back is an anchor point for several muscles. It doesn't sound like nerve pain. It could be a small tear in the facia/ligament. The lats anchor in the lower back as well as the erector spinae. If there's a knot there it could be a bad spasm. Valium or Flexaril are great for that. You said you've been icing the area. I have many freezie packs. various sizes and types always in the freezer. I hate icing my back but it really is the best thing you can do.