I ran across a large Northern Green Frog, Rana clamitans, that kept jumping vertically in front of my car and landing with an uncoordinated splat. It kept it's head held high and cocked backwards so I figured spine damage or maybe something neurological. If it was an injury, it looked old since I couldn't find any recent signs of trauma so I shuffled it off the road and into the nearby swamp. It seemed to swim all right. I didn't feel at all bad leaving it behind, and neither should you- nature will do her thing if they were too severely injured to carry on normally.
About the habit some treefrogs have of clinging to you when picked up, I always figured this was the Millenium Falcon style of escape. The scary thing trying to eat you (such as a Star Destroyer) can't find you if you're stuck to it, so stay stuck to it. When you get a chance, float away with the rest of the trash and make your escape.