Seems to me you are really asking two questions: what is the legal definition of neg driving, and what should I say on my application? I can only answer the first, the second is up to you.
Assuming it was neg driving in the first degree (second degree is only an infraction), that is a simple misdemeanor. Unless the sentence was deferred, then it should appear on your criminal record, as well as your driving abstract. You may well be eligible to have it vacated. Talk to an attorney near the court where the conviction took place. Can happen in a matter of weeks, then you are legally allowed to answer the question, no. I have never been convicted.
You are right to disclose the negligent driving. This charge is a misdemeanor and needs to be disclosed. I am not familiar with the requirements for med school admission, but for law school and the bar association, the main concern is with honesty. It is far better to disclose the crime and explain it than to try to minimize or hide it. It doesn't seem as though you have given too much on the application. You may consider disclosing the amount of alcohol treatment you were ordered to complete. This is typically an 8 hour class and a victim's impact panel.