Just saw this.
Here is what I would do.
First, a good duck vet would be ideal. But in the meantime . . .
I would get her into a tub of lukewarm water. Stay with her, because she may have trouble floating.
My thoughts - is this an injury? Was a drake rough on her? Did another animal get ahold of her? Did her leg get stuck somewhere and she pulled it? Is she egg bound, with the internal egg pressing on a nerve? Is this some kind of toxicity, did she eat something toxic?
I would look for any clues that would direct me to what is going on - in water, can she move the leg at all? Is the leg coolish? Very warm?
I would feel all the way up the leg and compare to the other - if something is out of joint, that should be apparent.
Very gently feel her tummy - is there an egg in there? If so, extra calcium is needed along with about an hour in the tub. Extra calcium can come from calcium gluconate liquid, calcium citrate pills dissolved in water, even a Tums. I would aim to get at least 100 mg of calcium into her tonight.
What if it is just a bad pull? Then an Epsom salt compress followed by a good ointment if you have that.
Epsom salt compress. 2 tablespoons Epsom salt, half a cup of warm water. Soak a clean cloth in that. Gently hold the duck and wrap the cloth around the leg and foot. Wait patiently together for ten minutes if you can both go that long.
Do this twice a day.
Epsom salt is a laxative, do not let the duck drink or eat it.
Some members put the Epsom salt water into a flat-bottomed dish and stand the duck in it, holding the duck gently. Remember, no drinking the water.
I like to use comfrey and St. John's wort on the outside of the leg and foot for sprains. I have a cream called Traumeel that has those things in it, and I put a tiny dab on the leg at night (they don't swim at night). Traumeel is now reformulated as T-Relief.
I need to turn in, I will check messages in the morning, Lord willing.
Prayers for you both.