Joel,
In addition to Alan's information, I've discovered the burial site of Andrew Funk. He is buried at Point Lookout, MD in the prison camp cemetery. So it appears he was for a time at Elmira Prison Camp and then was transferred or his body was shipped to Point Lookout Prison Camp where he is buried.
Go to this link:
http://www.plpow.com/POWDead_F-K.htm#F
In addition, you mentioned Gettysburg. Andrew was wounded at Gettysburg in the fighting of July 2-3, probably on Culp's Hill. He reported to a hospital on July 5th and was back on duty pretty quickly, so I presume his wound was not serious.
Jim Martin