If you have an infection for almost a month why haven’t you gone to a doctor? You probably need an antibiotic to clear it up. Whether ointment or oral at this point. It is probably NOT advisable to be wearing any earrings at all if the infection has not cleared up after a week or two, you are only exacerbating the problem and if you are not sanitizing the earrings you can possibly infect the other ear as well.
As far as your eye is concerned, if you touch any infection and then rub your eyes, it could be possible that you are introducing the virus or bacteria of the infection to your eyes.