Hi,
that the cold pack helps suggest it's a muscle problem. I keep several cold packs in the freezer. They help. Ask your Doc before you try this, but this is what worked on my back pain. I would do a long soak in a hot tub. When I couldn't get to a hot tub; I would lie in a tub with my feet up, and the water as high and hot as I could take it. After the soak, I would do really gentle stretching, at first it would be more like gentle swaying. Speaking of stretching, there is a book called Stretching by Andersen. Might help.