I found a baby bird with a club foot in my yard years ago, and I nursed him back to health, though most people told me I should leave him and let nature take its course, but like you, I couldn't bear to leave him in the grass to be eaten! I named him Nietzsche- I put him in a little cage and fed him with an eyedropper, and after several weeks, he was big enough to fly away.
So, sometimes it works. Don't blame yourself if it doesn't since you can't know how badly the bird is injured. Putting him in a cage if you nurse him at home may help calm him somewhat, and a trip to the vet might well be too traumatic without a cage, so you should get one either way you decide

Keep us posted on how the little guy is doing- You have a very kind heart and I hope you are able to help this little creature!