As far as i know, stringy discharge can be caused by Vernal keratoconjunctivitis. And this often happen to children. People suffered from Vernal keratoconjunctivitis probably experience itchy eyes, sensitive to light, watery eyes and foreign body sensation etc. If you also suffered from those symptoms while you got stringy eye discharge, you are probably got Vernal keratoconjunctivitis. Anyway, you shall make a definite diagnosis by a eye doctor.
I think string eye discharge can be a sign of allergy. But if you only have stringy eye discharges, you may get a cold other than suffering from an eye allergy. An eye allergy often bought people with problems such as itching, redness, burning or clear watery discharges. Sometimes you will suffer from all of these symptoms. But sometimes you may just suffer from one or two of them. I suggest you to see an eye doctor first. Hope you will be fine soon.