Hi and welcome to the back board!
The short answer is "yes."
It's called referred pain when one part of your body causes pain somewhere else. It's common for a number of reasons, and hopefully someone more knowledgeable than me will see your post and explain it better, but here goes: you have nerves all over your body. Nerves in one area that get pinched or irritated can cause pain elsewhere. Examples: nerves in the lower back that are irritated can cause pain in particular toes. My severe scoliosis caused compression of my sciatic nerve and made my right leg hurt. Also, we tend to guard one area that hurts and put unnatural strain on other areas because of that. When I had a frozen shoulder, I had pain in my chest, my back, and my hip. My physical therapist told me to try to use that shoulder and arm whenever I normally would have, even though it hurt so much. That helped to reduce the referred pain.
Yes, GAD can cause pain. Stress can cause muscle tension, which can in turn cause pain.
You sound like a good candidate for a massage!
I bet it would relax you and at least temporarily give you some pain relief. For stress related pain, temporary relief promotes healing and moves you toward more long lasting relief.
I hope this helped. Do you have a good doctor?