I've tried picking her up, but won't put any wait one them. I added some more brewers yeast to their water incase it's a niacin deficiency. They are eating a home made feed. I've raised a previous flock on the same homemade feed and they did great.
How did she get her foot caught under the bowl? It sounds like the bowl isn't duckling safe and you're going to need to switch it out for something that is.
Try doing some hydrotherapy with her, allowing her to swim in warm water. Soaking the injured leg in Epsom salts may help as well.
Duck update. After swimming some last night and soaking on epsom salts she seemed more perky this morning. She used both legs to swim and seemed not panicked to be in the water. She also ate and drank. I'm super excited.