The ophthalmogist needs to exmine the lacrimal puncta to make sure they are open, look at lid margin to be sure it is in proper position and perform lacrimal irrigation to see if there is a physical blockage of the nasolacrimal duct. If this tear drainage system is in good anatomical condition then there could be excessive production of tears due to some type of allergy or irritation and a second opinion from another ophthalmolgist may be helpful.
There are many reasons one tears excessively including dry eyes, environmental allergies, blocked tear ducts. I would recommend that you seek the care of a corneal specialist if you cannot obtain an answer.
Sandy T. Feldman, M.D., M.S.
ClearView Eye and Laser Medical Center
San Diego, California