Sounds like Chronic Respiratory Disease (CRD) which is caused by mycoplasma gallisepticus (MG). Looks for a runny nose too. It's basically a sinus infection that backs up into the eyes. It it continues you'll see a hard cheesy substance form in the egg. They'll go blind in that eye when it gets that bad and it's usually a sign by then that they're not gonna pull outta it on their own.
You can treat with antibiotics but I suggest separating it and seeing if it gets better. If not, put it down. And I'd put bleach in the waterers if I were you to prevent the others from catching it. If you do treat with antibiotics, whether the various "cyclines", Duragard, or Tylan, you can pretty well expect to have to treat the bird fairly regularly. Especially during cold, rainy or snowy weather. Just one of the several reasons I cull and only breed healthy birds that never get sick.