I don't think it's a chicken but can't really tell from the photos - for its size the wings look very developed. I wonder if it's a little bird that was trying to fledge/leave the nest? Can you look up animal rehabbers in your area? Usually they specialize by animal type. The swelling is probably the water in the crop, depending on how much you fed it. If it is a baby bird trying to fledge and not used to humans it might be stressed out from all the handling. I'd keep it in a quiet room/box for now until you get in touch with a wildlife person or animal rehabilitator. I've gotten a couple of baby birds that have fallen out of nests before - if you end up keeping it, I'd try feeding it worms and also getting a recipe online for formula - try for parrot mixes if nothing else (monkey chow was one of the main components I used on mine but if you don't live in a city that might be a problem getting - soften it with water and feed little pieces.). Good luck - again, I'd let the little guy relax with not a lot of handling since you guys have already given him water etc.