Elongated styloid syndrome or Eagles syndrome usulay arises after a surgery or accident . You had any one these. ?The x ray you shown is rather not clear. You have to take another one to rule out that. And getting an elongated styloid all of a sudden is quite unnatural.
Next Steps
consult a dentist with suffucient x ray . you can take anlagesics if that much pain
Health Tips
you can have hot water pads over the pain area for mild relief