Pigeon won't fly or eat help!

Hello, Very happy to have found this website. If I am posting to the wrong place, or this has already been answered else where, kindly direct me. We have a pair of pigeons that returns every year to make their nest in our palm tree. When I came home on Thursday night. I found a pigeon sitting in my yard, with 2 of my cats closing in for the kill. I shooed them away and walked up to it. I very easily picked it up and saw that it had a small wound under one wing. We tried to release it and even though it flaps it's wings very well, it can't fly.
I work at a veterinary hospital (although we don't treat birds) Our vet gave me some oral antibiotics. It looks like a full grown pigeon. It does have some very small yellow feather sticking out here and there on it's head. It's eyes seem to be a light brown. not sure if this means it is a juvenile?
It flaps like crazy, but when it tries to fly our of my hand. it crashes usually on it's head or chest. I have seen it drink water on its own, but it shown no interest in bird seed. I have tried putting some down in my closed palm. It will nibble at it, but doesn't seem to be getting any of it. I have also tried making a soup our of A/D (a veterinary diet for debilitated animals) and offering it in the bulb of an eye dropper. Again, no interest. It walks all over the yard, seems alert, preens itself, but it is going on it's 3rd day with no food. I can feel it's breast bone, not sure if that mean s it emaciated. I can rehab a dog or cat easily...birds I know zero about. I have tried to give it food with syringe, but i can't get it to open it's mouth, and I'm afraid I will hurt it.
It also has zero fear of my dogs and cats. Not a good trait in a wild animal! I open the cage door, and it immediately climbs out onto my hand. Is there any chance that if I do get this bird to fly and eat, that I will be able to release it?
Any advise would be greatly appreciated! I am in Porterville, California