If you can get some oral antibiotics in her soon, it might be a good idea. The extra swelling may be due to irritation from the cleaning, and I would suggest not forcing her eye open when you do this. Instead, maybe try using a refrigerated wet tea bag (black tea, not green) as a cold compress as opposed to the water eyewash, followed up by a nice thick layer of neosporin over the lid 2 or 3 times a day. Tannins from the tea and the cold might help reduce the swelling. I'm no expert on chicken eyes, but I know tons about human eyes, and have learned that many eye problems can be treated similarly in both. You may or may not be able to save her eye, but with oral antibiotics, you can prevent a spread of infection.