I've used iodine like this:
Make a tea with distilled water, chamomile and - if you have it - calendula, it's very healing. Strain, let cool to body temp. Put a small quantity aside for the eye treatment, like maybe 50ml or so. I either drink the rest or give it a quick boil, add some essential oils and give myself a facial.
For the eyes, though: add a pinch or two of Himalayan salt until the salinity is close to that of tears (I taste - obviously, you don't want to contaminate the solution). Add 1 drop of iodine. Use a dropper in both eyes. It stings at first, but a few seconds later, it feels VERY soothing. I tried this to get rid of floaters - it did not work for what it was intended, but it felt great. I suppose it may have worked if I only stayed with it a bit longer, but it was difficult, because the tea spoils very fast and I had to make this fresh pretty much 2-3 times a day - repetitive tasks bore me to death. Perhaps I should try this again, with some CS in the mix.
For the styes, try mixing a bit of baking soda with castor oil, oregano and tea tree to the consistency of a paste. Use a toothpick to put it on the styes. Do it often. If it will work, the roots will get angry, red, inflamed and the styes will hurt like ***. I lost mine while sleeping. This mix worked on some styes, but not all.
If you want, you can try an old wives remedy, it's completely ridiculous, but it worked for me: take some condensed water from your windows and wipe the eye a few times. I had this done a couple of times as a child and never had an eye infection again - I should try it for the darn floaters.
Please let us know what works for you :)