I think you are probably correct in associating the pain you feel in Savasana (Corpse Pose) to your posture when on the computer. It sounds as if you hunch up your left shoulder, which often causes a lift and a tightening in the trapezius muscle. Many people do this, especially when they're tired or stressed.
One of the wonderful aspects of yoga is that it can vividly reveal a vulnerability that is more latent in everyday life, giving us an opportunity to address the problem through our asana. Sometimes, however, our asana practice can actually reinforce a chronic condition, and I think this is what is happening to you. Speaking as someone who has struggled with ongoing neck and shoulder issues, my best advice is to turn your attention to your shoulder girdle and really make it a priority in your practice.
Specifically, focus on using your shoulder blades to draw the heads of your shoulders back so that they don't collapse or round forward. Imagine your shoulder blades as a pair of hands resting on your upper back, and think of the hands moving down just slightly and then gently pressing in toward your chest. You'll find that your spine will be straighter and your neck will be freer, and if you do this consistently in both your practice and your daily life, I think you may find some relief from the problem. Of course, you don't want to overdo this action, since that can cause its own kind of tension.
I would also be especially attentive to the way you set yourself up in Savasana. Make sure that you slide the shoulder blades down and rotate your upper arms out. This will increase the openness across your chest and should release your neck and shoulder in the process.