what is the age of the dog?
how do you think the dog sprained the leg?
I had a situation once with a fore-limb injury on a young male. The short version is he loved to launch himself . No one asked him to . He would scramble up a big boulder and launch across the narrows of the seasonal stream . He would get onto equipment just to jump off it. One day he did this and all his weight landed on one forelimb. Carried on . Next day , favouring that forelimb a bit . A bit more the next , then nothing . Dog normal , back to being physically daring do . Since this was a dog in growth stage we could see that the limb was starting to have some deviation from straight and true . At pastern the limb would start toe out , limb seemed shorter .
So to the vet . X rays showed that he had damaged , essentially bruised his growth plate denying the blood supply for the bones' extension where the radius and ulna meet , one side able to grow the other shortened . The vet had to insert a rod and pins to enable bone to form around this so that the leg would be the same as the other.
In the end the dog was totally fine .
With young dogs you could look to panosteitis https://www.google.ca/search?q=panos...w=1263&bih=553
or you could look to what I had described.
this is the worry "concerned about what's happening to her other leg as a result. Because of the sprain, she's been carrying her weight on the good leg. That leg is now showing signs of carpal hyper-extension at the wrist. The wrist is around 45 degrees which seems pretty excessive"
It actually may be that leg which is the problem ??
any way I would visit the vet to get a diagnosis.
If it is a "sprain" then you can provide anti-inflammatories .
If it is some damage then you can catch it early before the rest of the anatomy isn't affected by compensating.