Hi @charid , sorry you're having a bad time with this. Your chick has a slipped tendon. I'm out of town right now, so it's hard for me to post.
It is definitely treatable (well, it is unless the chick has further injured itself or the swelling has cut off circulation, or other complications...)
Here's a thread from the peafowl forum where I posted pictures. I treated two peachicks this season (well, actually, the vet did the first one) and both recovered. What you have to do is straighten the leg (and with that, the tendon should either go back in or be able to be put back), then tape with a slight bend using a flat taping technique, giving the swelling a chance to go down AND the groove to deepen, which will eventually hold the tendon where it belongs. The tape will need to stay on for 4 to 5 days, with the caveat that as swollen as your chick's leg looks, you may have to deal with that.
Forget the sling. My peachick got out of every sling & chick chair I built. Vet said just let it be -- once splinted, they manage to get around on the other, and once they are up, the splinted bad leg will help hold them up. Just make sure there's soft places to rest. No little friends, unless there's a really quiet one that won't pick on it.
Here's the link, you are looking for post #12
https://www.backyardchickens.com/t/1092979/peachick-with-slipped-tendon/10
I wouldn't recommend straws, rubber bands or other splinting materials. The flat taping technique works really well and is how the vet did it. Also, DON'T use tiny pieces of tape -- I lost a chick to ingested tape, despite fairly heroic efforts to save it. That was hard.
Good luck. Use my name in post if you need more help, otherwise I may not see it right now, sorry!