From India, Mumbai
You committed a crime and you were punished for it. The completion of the punishment should put a lid on what happened in the past. An act of rash and negligent driving was committed outside the domain of company activities. It was not a professional lapse but a personal one. How long to carry the baggage of the guilt for the personal lapse is a point to moot.
Sometimes you need to break this shell of self-deprecation and face the world. Therefore, start applying for jobs vigorously. Sometimes your luck will click. However, in the meantime prepare yourself so well that the interviewer should feel guilty if they lose your candidature!
All the best!
From India, Bangalore