Coccydynia can occur from injury to the supporting ligamentous structures. These ligaments become painful with stress (such as in sitting). You could call this “tennis elbow of the butt”.
Normally, in referral pain, the area will be painful but not extremely tender. Pain is what you feel without provocation. Tenderness is pain generated by pressure against the area. In true coccydynia, pressure against the coccyx will be very painful.
You can have a steroid injection or PRP injection here to help calm down the inflammation. There are some greater risks with an injection here. The skin is thinner and steroids can rarely thin the skin even more or cause an ulcer. This area obviously has a higher bacteria burden. Infection after injection is also possible.