Oh hey!!! Our black Minorca looked JUST like this on Monday. I keep posting this same story. Anyway, swollen on one side...ours had a runny nose though and it was a bit stinky. Checked symptoms here, became freaked out by what it could be, bleached the neighborhood, went to the vet. Vet said a secondary infection from dust or allergies, possible sinus. However, whatever was in the face and eye was draining through the nose and not smelling like roses. He gave her a shot, linocine or linocyn, something like that. I read and read here, and began washing both eyes with grocery store saline solution and then totally gooping both eyes with plain neosporin oinment (with no pain relief ingredients, that is dangerous to hens. The plain ointment has almost the same ingredients as opthamolic ointment, so it was posted here. I checked my cat's tube of stuff from last week, and it did have the same active ingredients.). She is isolated as the vet wanted to be sure we could identify her eggs since she had the shot. Today, she looks just about normal.
Also, I read garlic and cranberry soft gel caps are good for birds with possible infections, virus, things going on. Search on those two items, there is lots of interesting stuff.
Good luck!