It's not conjunctivitis - that is the good news. My now 1 year old had the same thing. The bad news is that it is some kind of infection but it is easily treatable with Erythromycin optical ointment which you have to see the doctor for.
I found that the best way to treat it was to apply warm wash cloth to the eye(s) a couple times a day to clean off any build up and WASH YOUR HANDS A LOT and DON'T PICK AT IT. Yes, it is very sticky and hurts when you pull it off.
Thankfully the infection cleared up quickly with my girl and we have not had a reoccurrence of it since. If I had to guess, I think it may be infection/irritation of the tear ducts due to the infection/infectious mucus from the sinus'. Anyway, it's common and clears up easily with eye ointment.
Hope this helps :)
~E. St.Clair
aka:____@____.com
Mother of Fiona-3 and Abigail-1