Has she always had this pop-eye (lol Popeye's chicken)? If she has, then it's nothing too serious. And even then, sometimes the problem doesn't show till a few weeks later. There are occasional genetic mutations in chickens that cause the cornea to become misshapen. Often it barely hinders their vision, and causes no discomfort. Her eye looks clear and healthy other than it's shape. It has no inflammation, no infection (that I can see), and doesn't seem to cause her pain. That's why I'm guessing it's just genetic. She probably shakes her head because she gets dirt or some debris in her eye occasionally (it's literally popping out, and it's hard for her to shield). So all you really need to do it keep an 'eye' on he to make sure that it doesn't get damaged or infected. Any cloudiness, hindered of vision, or redness/swelling will be cause for concern. It'll be better to catch injuries early on. She just needs a little extra watching!
