It is both overreacting and a valid feeling. If you were not wanting to drive before tue accident, then the accident escalating the feeling is a valid response. People not wanting to drive is not that uncommon! I love to drive but my daughter resisted learning for the longest time and is only learning now because it is a necessary skill to have in this country if you want to visit 95% of it because of how transportation is structured.

Your father is also right that an accident is not uncommon and assuming it was low speed it shouldn’t keep you from continuing to try, although sentiment requires wanting to drive.

You can live your life relying on others to drive you around, although that approach is limiting. Keeping up the ability and confidence to continue driving in case you need to might be an important skill where you live, and that would be the only reason I would encourage you to keep at it. If public transportation, biking, or walking are feasible for most of your travel needs then not driving is a reasonable choice!