Dog attack, rooster not standing up... no blood, but possible broken leg and/or back?

Sorry, I have no clue about anything when it comes to chickens so you'll have to be patient with me; my mother is a brand new chicken owner and I'm just trying to help her out because she's crushed that her chickens got hurt.
My aunt's dog recently snuck into my mother's chickens while we weren't looking and attacked them. It killed one, and another one refuses to stand up. When we first got to them and got them away from the dogs, we noticed the dog had bitten it on the back (although there is no blood whatsoever on the rooster, so I don't think it broke the skin; is it possible for a chicken's back to break from a terrier bite without its skin breaking first?).
The rooster's mouth was open and it was fully aware of its surroundings, but it wasn't making any sound. So fearing that it had maybe broken it's back, I tested out its legs. The right one moves in a full range of motion and can clutch with it's foot; the left leg has a full range of motion as well (and when I moved it around, the rooster didn't make any pained noises so I don't think it's in pain?), but the leg is limp and the foot doesn't clutch.
Eventually the rooster closed it's beak, and it didn't seem to open it more than a small bit when I tried out the limp leg a second time. It has made a small amount of sound since then, but for the most part is silent (it was a pretty quiet rooster before, so the only change is it being quiet and limp when picked up).
I felt along its back, and it does have a bump on its back that I don't think was there before (I don't handle the chickens much, so I'm not sure), but maybe it's just swelling from the feathers that got tore out; either way, the rooster has shed a few more feathers in the area it was bitten since then. But it's right leg works fine, if a bit sluggishly.
It's still a baby and hasn't even begun to crow yet, and my mother was devastated by the one that was killed so I'm really hoping that there's some way we can save this bird; she'd be miserable if she lost this one too, because she's seriously attached to these babies.
It's currently with a baby chicken and another baby rooster, but these birds seem to be acting very protective of their injured friend so I don't think they'll be an issue.
What's wrong with this chicken, and is there anything we can do to save it? I can include pictures, if needed.
Thank you for all of your help.