Hi jmilanski,
A back issue is normally from the spine being out of alignment over the course of the night and could come from a mattress that is either too soft or too firm. It’s more common for back sleepers that it’s caused by a mattress that is too soft (which lets the pelvis sink down too far) but for side sleepers it can also come from a mattress that is too firm and causes you to “twist” away from pressure which in turn puts the spine out of neutral rotational alignment.
Post #2 here has some information and links to other posts that can give you some insights into what may be happening in your case and the tutorial post here also has more information about testing mattresses more accurately and objectively for PPP (Posture and alignment, Pressure relief, and Personal preferences).
Back pain is generally a sign that you are out of alignment yes. If you replace the bottom layer with a softer layer then it would soften the support layer in the mattress and would help if the support layers were too firm but I would think this would have a lower probability of success … especially if your mattress is too soft already.
It may be worth trying the mattress without the wool topper just to see what happens because any differences in your experience between two different combinations can provide a clue to what may be happening.
Phoenix