The information provided here is not a replacement for a doctor. You shouldn't use it for the purpose of self-diagnosing or self-medicating but rather so you can have a more informed discussion with a professional TCM practitioner.
In Chinese Medicine tear ducts inflammation can be treated by one herbs that we have on record. Here is the list below.
Because it is a herb specifically indicated to treat tear ducts inflammation as can be seen on Rough Horsetails's page.
Its main actions are: Disperses Wind and Heat and relieves the eyes. Stops bleeding. Diuretic.