The best eye wash I know of is borax in water; I have used it on a few kids, taking away soreness, redness and infection within minutes to a day or two.
Dissolve borax in warm clean water (approx 1/2 teaspoon to 20 ml of water) then put a drop or two in the eyes. Important that it is body temperatured; to cold or warm will not be comfortable.
Borax has been used as eye wash since antique times and is added in most products even today. Very safe.
I would not put Iodine in my eyes, even if it is diluted, but it is great to put on your skin as you mentioned.
Ps what I know from chinese medicine is that swollen below eyes are very kidneys related; how are your adrenals ?; they have a big say in water retention / swollen; and are better with salt.