A vet is best, and not always possible.
Take a look at this. Ducks often can recover from serious injuries, much better than we thought. See if you can determine the exact nature of the injury. Also look for hidden puncture wounds on all of them...
Saline solution, Epsom salt solution, both kill bacteria.
The best thing would be veterinary care, I don't want that idea to get lost here.
In the meantime and if you cannot get a vet . . .
Here is what I would do without access to topical antibiotic or vet.
Get ahold of some St. John's...
Bumblefoot begins as a localized infection caused primarily by Staphylococcus aureus, a common bacterium. Same kind of bacterium causes acne.
Anyway, it is all around us, and ducks' immune systems generally take care of it. But for different reasons, sometimes it gets ahold. At the site of...
It sounds like a big case of bumblefoot, which is an infection of the foot and sometimes gets up into the leg.
If the joints are swollen, the infection may well be in the joint.
We need to talk about your setup, to see if it can be improved, but bumblefoot just happens sometimes.
To begin...