That sounds like the leg is popped out of the socket.... or broken way up high by the hip where it is difficult to see and swelling and bruising is hidden.
Since you have other chicks...
Pick up a normal chick and feel all over the hip area... keep doing that with your healthy chicks until your fingers get an idea of what is normal.
Then pick up the injured chick... see if you can feel what is different.
The couple times I have had a chicken break a leg way up by the hip.... I had to put the bird down. It is too high up to splint. I tried rest, and time, but the bone wouldn't regrow/stabilize so it was always painful.
If however it is a sprain, that can get better! Just last year I had a chicken with a very bad sprain... it took her over a month before she could move around properly. The chicken with the sprain was not in as much pain, as the chickens I have had with broken legs.
If it is a dislocated hip.... I have watched a bunch of you tube videos to fix that.... and I have failed completely... and those chickens with that affliction also were in too much pain, did not improve, and had to be put down.
I am very sorry I don't have better input.
Yes, super sucks.