When you consider that your tear ducts can drain into your sinuses and vice versa, it is not at all unusual to have eye slime (I get it a lot when my sinuses are going) coming from that eye.
Something that can make it seem worse though is if you have dry eye. When you are not having sinus drainage, do your eyes ever just itch constantly? This could actually be from dry air or allergies, or even any medication you take. Medications that list dry mouth as a side effect also tend to dry out sinuses and eyes.
I would say use cleansing and moisturizing eye drops (such as Visine) to help alleviate your symptoms. Also (this will help with the cold, potential sinusitis and/or allergy symptoms you posted about elsewhere), keep hydrated with lots of clear fluids and consider using a humidifier or vaporizer in your room at night.
Keep us posted!