Is your duckling in a brooder? if so what are the temps? Pekins are known
for panting They must get overheated easily I see it a lot on here. If you keep him outside is it hot there. The panting may just be he is hot. I'd definitely listen to his breathing put your ear up to his chest see if you hear any congestion. Get some Terramycin eye ointment and start using it on the eye if it doesn't look any better by Monday. Or have a vet look at him.
How is his appetite and is he drinking too and his poop is it normal?
You can rinse the eye with luke warm saline solution. I would also suggest a like warm bath. When I raised Pekins they had deep water but would often not dunk their heads. I had to give them baths to keep their eyes and nares clean. I had the same build on the eyes and saline rinses with baths cleared it up. Pekins are terrible at staying clean. Once mine moved outside with a permanent pool, it reduced the amount of problems.