Being arrested and charged is only an allegation. If you settled your case by pleaing to negligent driving, then the answer to the question if you have a DUI, is No. You might want to get a copy of the disposition of that case from your clerk of court to have in the event a background check shows the dui arrest and not the disposition, to prove how the case was resolved.
Not an immediate solution to your problem, but certainly something to keep in mind, is seeking to vacate your conviction. You would qualify 3 years after completing the terms of your sentence. This allows you, under the current statute, to tell employers that you have not been convicted of a crime. In addition, the conviction does not show up in a Washington State Patrol background check. There are some statutory qualifications.