Constant sharp pinching pain in my lower back. when i strain to have a bowel movement or cough i get a quick sharp pain that goes down the back of my right leg. long history of chronic constipation and am currently impacted. is constipation causing?

Constipation doesn't cause that symptom but the heavy strain during defecation aggravates the pinched nerve syndrome. You likely have pinched nerve syndrome (radiculopathy) which is usually called sciatica. This problem is usually self limited, i.e. resolving by itself, but it can recur and back exercise if the most effective way to treat. You should see your doctor for a thorough evaluation.