Oh dear...the first thing I would do is a flush through...feed your duck a sloppy bran and water mixture to move things through its system...
The mucky eye could indicate something else though....
Riemerella Anatipestifer Infection.
This bacterial disease of ducks is also known as Pasteurella Anatipestifer infection, infectious serositis and New Duck disease. Anatipestifer infection causes high mortality, weight loss and condemnation. In the acute form, listlessness, eye discharge and diarrhea are commonly seen.
Ducks show incoordination, shaking of the head and twisted neck. Birds are commonly found on their backs, paddling their legs. Typical lesions found in dead birds are infected air sacs, membranes covering the heart and liver, and meningitis. Preventive management and vaccination are effective means of control. Penicillin, enrofloxacin and sulfadimethoxine-ormetoprim (0.04-0.08% in feed) are effective in reducing mortality
Kim just in case your duck has some sort of infection happening it certainly would not hurt to give him a course of any of the meds highlighted...see which ones you can get from the vet...they should be able to tell you the correct dosage..
He probably has gotten a fright with the dogs and perhaps his immune system has been down a little...stress can make sickness rear its ugly head...these two things might have been all that was needed to make him sick...So I would go get some meds...do the bran flush...seperate him from any other ducks/chooks etc and see how you go..Post back again if you need anything else..