Your chick sounds a lot like my chick. Mine hatched on Sunday, and I noticed immediately it had curled toes on both feet and couldn't stand up. I made cardboard shoes for both feet, and hobbles. After a couple of hours, it was getting around, although not very well. Here's a timeline of it's improvement:
Day 1: Chick wearing 2 cardboard shoes and hobbles. Getting around brooder some, but falling over and getting stuck a LOT.
Day 2: Total improvement in left leg. Removed shoe on that foot. Chick eating and drinking, significantly less clumsy. Holding up right leg. Noticed swelling in joint and suspected slipped tendon. Splinted right leg.
Day 3: Left leg is strong. Removed hobbles. Chick balances better without.
Day 4: Removed right cardboard shoe, leaving only the splint. All toes are straight.
Day 5 (today): Chick is getting around really well, and actually bullying the other chick a little bit. Still won't put pressure on right foot. Joint still slightly swollen.
Despite all the reading I've done and videos I've watched, I still can't actually visually tell that the tendon is slipped, and I have no idea if it's back in place when I wrap the leg. I just gently pull the leg back (like a chick does when it's stretching), and kind of massage the knee joint until the leg straightens, then I wrap it to hold it in place. I unwrap it to check twice a day, and it always looks exactly the same. I can't seem to find many cases where a chick has fully recovered from this, but there are more cases where the chick grows up to live happily on one leg. I'm just wondering at what point do I give up on wrapping the leg? My other concern is that even though I see it eating and drinking all the time, it's growing a lot slower than the other healthy chick.
My chick also sleeps on it's side. I think it has to because of the splint. Sometimes it follows the other chick around and places it's tiny little wing on the other chick's back for balance. It's sad, but adorable. Overall though, it seems happy. It hops around on one leg, chirping all day, and scratching in the bedding.
Here's hoping both our chicks continue to improve!