Okay. Here I go......
I kept homers for many years. Sometimes my birds would come back really busted up from hitting powerlines at 40 mph, Falcons, shotguns.
A pigeon is a tough bird. Your bird will probably live, and if it flies again, it won't leave your home unless you take it into a big city 50 miles away.
If it doesn't fly, you've got a responsibility to keep.
Pigeons need water, in a bowl at least 1" deep. They stick their beak under and suck it in.
They will eat whole cracked corn - not crushed, whole kernal. Also, get a bag of split peas at the grocery store, like for soup. They must have grit. Big box pet shop or the feed silo will have this.
A good feed store may have formulated pigeon pellets. I kid you not. Pigeon racers are a fanatic bunch.
No crushed corn - this scratches the gullet and will cause infection.
Keep the water clean- they like to stand in it and as you soon will discover, birds have no sphincter control.
They like baths. A skillet filled with water and a hose misiting onto it (all in a cage) will make your pigeon happy. A happy pigeon flies home fast.
Knowing what I know, and having nursed wild and bred pigeons back from injury, I'd have left it for the cats.
