Can adrenal insufficiency cause mood swings accompanied by anxiety and pain in the chest?

Chest pain? The mood swings and anxiety are very commonly associated with adrenal and thyroid problems while chest pain may accompany the anxiety, it needs to be evaluated separately to rule out other causes including those related to the heart, lungs or stomach.
Unlikely. The main symptoms of primary, gradually developed, adrenal insufficiency are - chronic malaise lassitude fatigue that is worsened by exertion and improved with bed rest weakness that is generalized, not limited to particular muscle groups anorexia weight loss.