Some thoughts from my experience:
1) You mention your shoulders being outstretched and flexed when you work, that's a good place to start. When I work at a desk, I try to maintain a posture that keeps my arms parallel with my body until the elbow where my forearms then extend at a 90 degree angle or so. When I think of someone with their arms outstretched, it's hard for me to not imagine you're also leaning forward at least a bit which also puts stress on your neck. Aside from changing desks, you might want to look into an under-desk keyboard/mouse drawer/shelf to lower and extend those things to you in the correct position. You shouldn't be stretching to work at a computer.
2) Headphones. For me, hours wearing big over ear headphones can leave my neck and shoulders sore even when sitting with perfect posture. Consider using earbuds when you work.
3) Your bed. Most neck and back problems start in the bed, whether it's having a pillow that's not properly supportive or has dust mites, not turning your mattress often enough, sleeping on an old lumpy mattress or just sleeping in the wrong position. These things can all contribute to neck and back pain. Don't rule out the possibility that multiple factors could be contributing to your pain.
4) Light exercise with stretching/yoga. Can help eliminate lactic acid from your muscles contributing to the soreness.
5) Diet. This one's sort of on the low end of potential fixes but having too many foods that increase uric acid levels (alcohol, meat, dairy, fried foods, soda, etc...) could lead to joint stiffness in general or increased difficulty for your system in breaking down other acids that lend themselves to soreness like lactic acid.