The white over her eyes could be the nictitating membranes or third eyelids. Here is a good article with pictures: http://www.the-chicken-chick.com/2013/05/chicken-anatomy-nictitating-membrane.html
Yes, they have that membrane. I would get to a vet if possible, and in any case, start saline solution rinses 3 times a day. The duck person may be able to get some medicated eyedrops, and Vetericyn makes an eye gel also. Separate the drake - keep your duck girl safe. Give vitamins, electrolytes in her water a couple times a week for a couple of weeks, and keep us posted!
