Conjunctivitis is not always infectious and so we cannot say it is an infection of the eye however we can say it is an inflammatory condition much like the name suggests, one could have sterile conjunctivitis without and viral, bacterial or protozoan involvement, a typical case in seen in allergic conjunctivitis where the same redness and tearing is experience and yet still the eye would be sterile in that sense.

I say in that sense because our eyes have basal microbes living on it in the majority of the population though and these innocuous microbes can become obnoxious when the opportunity presents itself especially when the immune system becomes depressed. Great and intricate writeup, thanks for sharing