It is really dangerous to have this disease. You should use some antibiotic for it such as Low doses of tetracycline or Metronidazole. You can also wipe the area regularly with hydrogen peroxide. If still you do not find any change in its condition then take it to vet. May be there is something more that. It can be Glaucoma or Conjunctivitis, which needs immediate treatment.
Conjunctivitis - very common in kittens (and contagious ~ so keep kitten away from other cats until cleared up). Try using cotton balls soaked in luke-warm water (previously boiled to sterilize) and rinse eyes out twice a day ~ morning and night (more often can irritate the eyes and make them sore). Wipe gently from inner corner (by nose) to outer corner , and use a fresh cotton ball for each eye to avoid cross-contamination. You can also try cotton balls soaked in weak cool tea (no milk, no sugar), as the tanine in the tea is soothing. (If kitten is white, this may stain the fur, but that will soon disappear) If the eyes are not on the improve within 2-3 days, it probably needs antibiotics from a vet. Can never be too careful with eyes.
Runny or watery eye suggests that your cat caught some viral infection. Feline respiratory disorder and conjunctivitis (inflammation of eye membrane) can also be a reason behind it. So you should consult a vet as soon as possible.
