Have you taken this bird to a vet to identify the problem? Is it a broken wing, or just a sprain?
Pigeons take a lot of space. In their cage, they must have a ledge or box near the top of the cage. if the bird is unable to fly, make a ramp or staircase for it. A pigeon cage needs to be pretty good-sized, four feet long, and three feet high at the bare minimum. pigeons have softbills, so toys like shredders and colorful bells are not in their best interest, and could just scare a wild pigeon. you can still put colorful sticks and wooden toys to give him something to look at, but don't be surprised if it doesn't use them.
As for diet, my pigeons get a high-quality mix but many wild bird seeds from the store work well, and you can find lots of good feeds online. make sure to include bits of greens as well, just little slivers small enough for the bird to eat.
I would very highly recommend you bring the bird to a vet, to be treated for parasites and have the wing looked at. But please take into consideration that if the wing is broken, the bird will never fly, and you HAVE to spend time bonding with the bird so that it can be able to do things and not sit in a cage all its life. Pigeons are extremely smart and can get bored easily.