Sounds like a nerve is getting tweaked. It could be as simple as posture when you feel stressed. If you sit with your shoulders pulled up to your ears, which many people do when stressed out, then the muscles get tight between the shoulder blades, and can put pressure on nerves in your upper spine. Then when you sigh, you take in a big breath, and expanding the ribcage, lifting the shoulders and a nerve is getting tweaked when you do that. That's my guess.

Other things that involve nerves:
Herpes neuralgia, almost always the left leg only.
Vitamin deficiency: copper, B12, B1, B6