Iv burst the bursa sac in my shoulder, why is the pain so severe my left hand side of neck, back and arm are continuously achy. How long for recovery?

Be rechecked. If you are experiencing severe pain on the left side of your neck down into your arm, it is probably more than a simple injury to your "bursa". Among possible causes which could be checked for would typically be a pinched nerve in the neck, a torn rotator cuff, or signs of cardiac ischemia. A detailed history, exam, and appropriate studies would likely result in an accurate diagnosis.