If you just had simple viral conjunctivitis, it should have cleared up within 7 or 10 days at most. Therefore, if you are still having symptoms it might be worth seeing your primary care doctor
just to make sure something else is not going on.
For example, you may actually have had an allergic conjunctivitis, rather than an infectious conjunctivitis. In this case, the conjunctivitis will not clear up unless you avoid the provoking allergens (such as dust, mold, mites) and perhaps take an antihistamine medications.
Sometimes, persistent tearing can represent a scratch or other trauma to the eye, especially if their is blurring of vision, pain, or sensitivity to light. If you have these symptoms, you should see your doctor as soon as possible, given how long the symptoms have been going on for. Sometimes scratches can become infected or may not heal well, leading to ulcers or scarring which can permanently affect the vision.
I suggest setting up an office visit with your primary care doctor as soon as possible to figure out what is going on. In the mean time, avoid touching or rubbing the eye as this can cause more irritation or damage. You may want to apply saline drops to keep the eye moist.