Hello, I'm Dr. Bob.
I'm sorry to read of Pickle's breathing difficulties.
The information you've found online about the connection between breathing sounds and iodine is essentially correct, but since you've already been supplementing her with iodine already, it is not a likely diagnosis.
More likely is an upper respiratory infection which can also cause exactly the signs you're seeing.
A possible contributing factor to her illness may be her diet. If she's on an all seed diet (other than the iodine supplement) she may be developing a nutritional deficiency. This can lower her resistance to bacteria, viruses and fungi in the environment allowing an infection to become established.
Birds prefer seeds to all other foods, but seeds don't provide all the nutrients they need for long-term health. Fresh dark green leafy vegetables like Swiss chard, spinach, kale, collard greens, cilantro, parsley, carrots with the tops attached, yellow, red and green bell pepper strips, dried chilies, cooked squash, pumpkin and sweet potatoes are all foods that add vitamins and nutrients and should be offered to her. It may be tough to get her to accept new foods at her age, but it is definitely worth trying. Pelleted food like those from Lafeber or Kaytee are very good as basic diets, but are unfortunately, not available everywhere.
She needs to be examined by a veterinarian with avian experience, if possible, and most likely needs to be on an antibiotic, to help her fight off the respiratory infection. Do no delay in seeking help for her, as birds instinctively hide their illnesses to avoid being singled out by predators in the wild, and are often quite advanced in an illness before they begin to show symptoms. It may be later than you might think.
If you should have further questions, please let me know.

You're most certainly welcome, best of luck to all of you!
Dr. Bob

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