RE: HOW TO KNOW IF YOU HIT A DEER
Arched back says gut shot to me. Did it sound like a pop or slap? Ribcage shots usually sound like shooting a pumpkin. A hollow, squishy,thud sound.
The deer should bed down soon after being hit. Since you did not push it, you should find it in less that 100 yds.
Tracking may be difficult with the lack of a blood trail but go by tracks, up turned leaves, scuff marks, etc... Look in the direction of water. Also check out thick tangles or heavy brush.
Let us know!