What do you mean by breathes heavy? Does his tail bob up and down when he breathes? And shivering? Are you sure he's not just like fluffing and shaking at the same time to straighten his feathers out?
If they are molting you will start to see more feathers around the cage. Lots of fluffy ones and maybe a flight feather or tail feather or 2?
Like superstar said, there is special seed mix you can get to help with molt. It comes in a can and is called Molting supplement. Also warm bathes or misting helps.
If you are worried Dee might be sick, call your vet and ask what h/she thinks. Keep an eye out for other symptoms..eating less, less active, runny poo or less poo,funky colored poo, sneezing. I know it's soo hard with birds isn't it? Seems like we worry over every little thing