I cannot believe it's an injury from the fence.
I have two rescues being slowly introduced to my ducks. After 2 weeks isolation in my Florida room, they are now coming out into a temporary dog exercise pen on my patio. The bars are barely wider than my ducks' beaks. yet I heard a commotion and went to check and one of my pekins had his whole head and neck through the bars [with the two newcomers pecking him furiously.] My duck looked like he had stuck his head and neck through three gaps run together, but no he had managed to get through just one gap in the bars. It was very difficult to get him back through the gap it was so narrow. But when I got him back, he came for a quiet sit with me for 10 minutes but was then 100% back to normal. No wounds on his head, neck or shoulders. Something else happened to your duckling. Is there a dog around?