What's the swollen area feel like - solid, squishy? I know she won't like it being touched, but if it's just hard and swollen, it may be due to inflammation rather than infection.
Her foot looks similar to one of my older goslings' - goslings are big goofballs that zoom around without paying much attention to what they're zooming into, and one ended up with a foot that's swollen right in that area (not bumblefoot). She would not use that foot, at all, it was pinkish in that area and felt swollen and warm to the touch when I examined her. I suspect that she tripped and sustained a bad sprain.
I've isolated her and have been doing daily "water therapy" - letting her float in warm water - and she's begun using that foot more. I'm also offering a vitamin supplement in water for general support and sprinkling glucosamine/chondroitin/MSM from a capsule on her food to help with the inflammation and encourage healing.
In my gosling's case, the injury looks like it's going to have a slow, gradual recovery. If there's no wound on your duck's foot that would indicate where bacteria could have entered, along with no other obvious signs of infection, I'd start conservatively and treat for a sprain. If it's that kind of injury, you should see some signs of improvement in a few days. Best of luck!