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 painful gums can be treated by one herbs that we have on record. Here is the list below.
Greater burdock root might help with painful gums
Why might Greater Burdock Root (Niu Bang Gen) help with painful gums?
Because it is a herb specifically indicated to treat painful gums as can be seen on Greater Burdock Root's page.
Greater Burdock Roots is a Cool herb that tastes Bitter and Sweet. It targets the Heart and the Lung.
Its main actions are: Relieves the Exterior and disperses Heat. Reduces swelling and clears pathogenic Heat.
Other symptoms often associated with painful gums
Coughing Swellings Sore throat Rheumatic athralgia Lumps Carbuncles Conjunctivitis Hemorrhoids Rectal prolapse Common cold