I had a chick that got a leg injury too at about the same age. She was run over by the other chicks. I thought we would have to cull her. But we built a "hospital"for her. Basically it was a small box covered with hardware cloth and placed it in the brooder. (I have a fairly large brooder) She had her own food and water and heat. She was happy with this arrangement because she could see everyone. She continued to eat and drink so we kept trying to help her. I gave her a small sock rolled up beside the harare cloth. She would sleep on top of it right by the wire so she was close to the others. After about a week she seemed a bit better and she was squawking for the others. So we put her back with everyone and she is fine. Wouldn't know she was ever injured.
But I also looked at slipped tendon. Hope yours gets better like mine did.