Hi HeyFaHey,
Tightness in the low back can often be an alignment issue – either from lack thereof from your sleep surface or due to your own physical limitations (strength, flexibility…) or a combination of both. Flipping your mattress over should be able to pinpoint if a firmer surface comfort could be a culprit here.
Do you have it on an actual coil box spring unit? If so, this would be in appropriate for your mattress. Or when you say box spring, do you mean a foundation as described in the foundation thread here? Some type of a foundation is what you would need for your mattress. Also, make sure that whatever bed frame you are using has a proper center reinforcement to prevent the foundation and mattress from sagging for any full, queen or king size mattress.
Again, I unfortunately can’t predict what might be causing this issue via an online forum. The links contained in post #11 here do provide quite a bit of good information about diagnosing possible reasons for should joint pain. This can come from a mattress that is too hard, and also from one that is too soft. It can also be a result of poor alignment due to your pillow not being the proper height, so you may wish to check that so you have a more neutral alignment when side sleeping. It can also be from physical limitations and impingement in your axillary area due to personal flexibility/structural issues.
It will be interesting to learn of your response sleeping on a firmer surface after a week or so and if there is any change or improvement.
Phoenix