I had a similar situation this year also. The buck I took was lame on the left rear, hit by and was apparently surviving an arrow shot (arrow looked to skim between the ribs and skin, lot' s of green puss though), and he was gut shot. Put him down, about a 170 yard shot.
I am still proud of the hunt, because not only was it a good deer but it was the right, ethical thing to do.
Robbie