There was a field hospital at Fortress Monroe. I know it because my GG grandfather wrote a story before he died about the war and what happened to him. He was in the 1st Texas Infantry Regiment. This portion is from after the Battle of the Wilderness:
"After this we continued skirmishing until October 7, 1864, when we attacked the enemy's bulwarks ten miles east of Richmond. (He's talking about the Battle of Darbytown Road). Here a Yankee bullet struck me just below the knee, breaking the bone. I was captured, taken to the field hospital and my leg was amputated. Was then taken to the Federal hospital near Petersburg where I was well treated by good, kind nurses. Was taken to Fortress Monroe where I remained seven months before I was able to travel."
He was paroled from Fortress Monroe at War's end and began the slow march home to Texas from there.