She may have vent gleet if so then you'd most likely need meds to clear it up.
some info http://www.duckdvm.com/condition/vent-gleet
https://www.tillysnest.com/2012/12/vent-gleet-prevention-and-treatment-html
Have you tried Prep H on her flesh around her vent? or hydrocortisone cream or ointment? it is supposed to help with getting swelling down. As for the calcium deposits, some of my chickens and ducks do have them on their egg from time to time. I don't do anything about them.
If you can post...