I wonder if you need to be so specific. Something like " I took a medical leave of absence from xxxx to yyyy due to injuries from a traffic accident. " As you say, let them fill in the spaces. The specifics of your injury are a private matter as long as you have been able to successfully return to teaching.

You can continue the rest of the personal statement as if you were never injured. Dwelling on your injury will only draw attention to it. It may also imply that you are focused on your injury and not your job. They want to hear about your teaching.

My best to you.