Here, feed stores sell antibiotics. It is something to consider. Parasites can also cause problems, and medicine for that can be found at feed stores.
Wondering if @Lacrystol has any insights.
Sounds like she has an infection and really needs to see a vet. Probably dehydrated, too, and a vet can get fluids into a duck quickly.
If there is no way to get to a vet, I would consider starting her on antibiotics - oral - a.s.a.p. Give her something like Poultry Nutri-Drench in her water...