The black spot on the gum seems to be normal pigmentation in the gingiva but a small dark spot on the same tooth at the top position is visible and it is a caries. This caries can leads to minimal sensitivity which you feels like mild pain.
Next Steps
Restoration of the tooth has to be done from a Dental surgeon to avoid further progressing of the Dental caries.
Health Tips
Avoid cold and sweet food and drinks for a while to avoid sensitivity or pain, till you consult the dentist for restoration treatment.