A bird in the hand...should be in the tree

We have another feathered visitor. Funny thing is I was visiting with the neighbor across the street and she was telling me she saw a baby bird on the ground and had gone in to find some gloves and came out and it was gone. I was thinking it was good because we'd end up with it and we're not having a lot of luck nursing them back to health. Not even 20 minutes later our dog went nuts barking in our back yard. Paul went to check what he was barking at and there was a small bird on the ground by a bush. I think he fell out of a nest in the Cottonwood trees. He has feathers rather than down, but I'm not sure he is old enough to fly. He didn't seem to be doing so good. Paul checked his wings when he put him in the box and there is no noticeable damage, but he was breathing hard and fast. I think he is frightened out of his mind. He was just sitting there this morning under the lamp, his breathing looks better. I guess we'll see how he does. I have no idea what kind of bird he is, just soft brown. We also have a little squirrel that's been around for about a week. We've seen them from time to time over the years, but lately this ones been out every morning squeaking up a storm. He sounds like a dog chew toy. I think the dog thinks it's a chew toy that is out of his reach and tauting him. The squirrel likes to sit a few branches up from the porch and squeaks for about ten minutes every morning. I kinda like him.