The Latissimus Dorsi (Lats) can become short, stiff and fibrotic due to longstanding postural tension around the spine. The Lats originates from the spine, Thoraco-Lumbar fascia, and posterior hips, and attaches on the Humorous. It is responsible for extension, adduction, and internal rotation of the arm. Hence if the Lats are tight it can limit your mobility in abduction/reaching over head and external/outwards rotation of the upper arm.
So, if this muscle has been chronically tight as a part of postural tension from guarding a sore back then in some cases it can be permanently scarred and tight. In these cases, it can make it hard or even painful to reach overhead even when the underlying spinal issues have been addressed.
Here is a self-myofascial-release exercise that you can do with a tennis ball to help to free up the Lats:
Setup: Stand next to a wall with your arm outstretched overhead.
Place a tennis ball just behind your armpit, in between your Lats and the wall.
Performance: From the starting position slowly roll the ball up and down along the outside of your armpit. Feel free to flex and extend your knees to increase the range of motion.
Roll for 30–60 seconds, and then switch sides.
If needed you can use a harder ball to increase the pressure.