Body and skin sore to touch/achy after a month of high stress and anxiety. Can a relief of anxiety cause body tenderness?

The opposite is true. If I'm understanding your question correctly you want to know if RELIEF from anxiety can result in body soreness/tenderness. Actually, it would be more likely to be the opposite. Anxiety of a constant or prolonged nature heightens sensitivity of the NOCICEPTIVE receptors in the skin and muscles (pain receptors) and tend to increase painful sensations. Relaxation should reduce pain sensitivity.