I have them as well. Lower back on either side of my spine. Small ones have sprung up further out toward my ribs and upper back. Thats nice of you to rub her back as yes they are very painful and cause radiating pain. Mine hurt though terribly when touched. No one has explained why they happen though, have you any news on that?
It is possible that the "lumps" are fat deposits under the subcutaneous tissue that are benign lipomas. If they move easily with touch and feel soft and do not cause significant pain with pressure, they usually do not require any treatment. If they grow in size and her discomfort increases secondary to where they are (close to nerves, etc) they could be removed surgically. Based on the description given, it would probably not be necessary for numerous lumps to be removed, if any. I'm not familiar with the terminology of "stress balls", but it may be helpful to evaluate the times when these lumps become more visible and see if there is any connection to activity, fatigue etc.