You always have the right to approach the court regarding any errors in the disposition. This would be a good example of one as a conviction carriers points and effects your job, whereas the withhold has no points.
Generally, a defendant will waive his right to appeal the plea in the plea agreement. A defendant can appeal a plea agreement only if it was entered into involuntarily, unknowingly, or without knowledge of the consequences of the plea. Have a local lawyer in your city investigate.