I treated a pullet for eye worm.
My posting may be the source of the bicarb + boiled water that the earlier poster wrote. I had gotten that from 'online vet'. I had not seen that anywhere else on the internet. I made the joke...pullet $10, vet cost $30....
Subsequently I did use Vet Rx according to the package directions for eye worm. Rather than be just like vicks the process turns the chicken upside down and uses a Q-tip in the V in the top of the beak. (Not sure ducks beaks are the same as chickens). The liquid flows through the sinus and drips out the top of the beak and flushes out eye worm. I believe that a couple of applications of that disintigrated the eyeworm.
I found through much research, a product called Oxy-Rid. Two drops in the eye cure eye worm, and one drop once per month is a preventative. So now I drop a drop in each of my hens eyes when I give them a monthly inspection and do all the health related routine that I do for them.
Oxy rid can be obtained from New Tree which is located in the Phillipines. They eye drops are about 5.00 btl. But the shipping costs are about $68. I said that I was going to contact a vet supply to see if someone in the US could stock the product. The shipping costs would be about the same for a case as for one bottle. I think the shelf-life is about 1-year. When I was talking to a vet about another matter he told me that the ingredients in OxyRid are not approved for meat birds in the USA. There is no egg withdrawal with the product however, and it is safe for chicks.
Here is a link to the older post. At the time I was panicked and thought that my pullet would damage her eye or some serious long-term consequence would result.
https://www.backyardchickens.com/forum/viewtopic.php?pid=6469194#p6469194
The eyeworm larvae needs 4-months from the time the cockroach eats eyeworm egg in poop to the time the chicken eating the cockroach is exposed to larvae that can infect it.
For your duck, I would check with a vet if possible and use Vet Rx to flush the eye worm out of the eye, if that is what is causing the problem. Good luck, i hope it is cured quickly.