Without being there or being a vet, I can offer that if it's a pull or a sprain, that Epsom salt compresses help quite a bit.
And, those kinds of injuries can take more than a week to heal up completely.
I have Runners, don't know anything about Mandarins (might someone on the Ornamental forum be able to help?)
But we have had a few sprains, and I use Epsom salt compresses followed by a tiny dab of Traumeel or T-Relief rubbed into the leg. Also as much time floating in lukewarm water as possible to take weight off the leg and strengthen muscles and improve circulation.
Some vitamin supplements may provide a boost to the healing process as well.
Please keep us posted. Ducks can recover from some awful injuries.
If you can get a good duck vet's help, that would be best.