Yes, it is possible that after enduring a 10-inch constant rain that their immune systems were lowered and something could have made them sick. The wet conditions that follow also invite illness (coccidiosis, fungus issues, toxin issues if there are puddles with stagnant water, etc).. And of course there are the mushrooms and other sorts of wet/decaying vegatation.
If you grasp some of this chickens feathers in your hand (around her neck or legs for example) do any of them come out easily? IF they do, then you have a case of botulism in combination with the other symptoms you've described. Botulism is VERY tricky to treat and the flushes that you use to flush the toxins absolutely must be followed up with electrolytes as dehydration is very rough on a bird, much less a terribly ill one.
However, this could also be one of a number of other things - including viral (brought on by the lowered immune system), or fungal (brought on by the environment), bacterial (respiratory and/or digestive - either of which could have been first), cocci (coccidiosis blooms in rain situations and diarrhea fits that as well), or just toxins - particularly if she had opportunity to drink from puddles that washed in toxins from others' yards.
First off, rehydrate the bird, correct her electrolyte balance by offering her vitamin/mineral/electrolyte solution for poultry. You must replace those electrolytes after using epsoms. You must also replace some of her good bacteria in her gut to help with the diarrhea. Personally I'd recommend acidophilis tablets from the vitamin section of a 24 hour store like
Walmart. It will be less harsh on her system and a smaller amount thus easier to give. But in a pinch, you could alternately use plain yogurt. (Which reminds me - in a pinch you could use pedialyte or gatorade to replace some electrolytes).
Moisten the crumbles with the electrolyte solution before you offer them. Mix the yogurt into the water/electrolytes you use to do that. This won't cure her -it will help her system to readjust if it's possible to do so.
On the Duramycin, at what dosage are you providing it? When you say you hear her breathing, does it seem the noise is coming from her head/throat/nose, or her chest (use your ears and hands to locate the source of the vibration that causes the noise). If it's upper, duramycin might work. If it's lower, you might need a different antibiotic as lower respiratory infections (if this is even a respiratory infection) respond to different antibiotics.
Did these symptoms occur literally overnight? Or at all over a few days?
