A friend of mine told me there is an ointment you can buy at the chemist without prescription, and it cleared her toddler's up in one night!
However I went to the GP for DS, as he has conjunctivitis last week, and we were prescribed antibiotic eye drops.

In the meantime, before you decide what to do, you can keep rinsing your eye with cooled boiled water with salt added. I once treated my own conjunctivitis with just salty water and it cleared up within a couple of days...