Advice please on injured pigeon!

I've picked up a pigeon and am trying to help it. It has limited use of its head. It was literally rolling around in the rain. I've briefly checked it over and it has minor skin wound to it's back. Bruising around its neck. One eye lid looks swollen. My initial thought was to euthanize but after reading into its prima facie injuries it's possible it will recover. I want to do the best for him or her. I can set up a recovery cage etc for it and do have some pigeon friendly treatments available but obviously can run to a pet shop for other things. Does anyone have any experience of this type of injury?