My Dad told me about some of the awful results of those battles when taking me with him to the battlefields, such as the men screaming their heads off while their wounded limbs were being amputated by saws sans anesthetic. Then the limbs were tossed out the windows onto the ground below. Dad actually took me into one of the houses — a tourism site at Manassas Battlefield — where these gruesome surgeries were performed.
Kind of a myth. Neither side ran out of ether except in the rarest of cases, mostly in the western theater. Same with morphine, the south had imported plenty of the stuff. . Even the South had a lot of both on hand in the last days.