You need to take your own time/pace. Pushing discussion of trauma can easily retraumatize a person.

But at this time you probably already have a "set story" that you tell, about the event..and can get through that by rote, am I right? It takes retelling and retelling and adjusting the info, adding some details and telling it some more... but not at every session, and often therapy includes how the trauma is affecting all other aspects of your life and how to realize this, and cope.

Discuss your fears about therapy with the doctor, and especially that you don't wish to leave the session without being ready to go out the door. It can take PTSD patients longer to adjust to going from therapy to the real world.. sigh.