If you pled guilty to a reduced charge, you have still been convicted of the lesser offense and the conviction is ineligible for expungement from your criminal record unless you participated in a judicial diversion program.
I agree with Kevin. The only way in Tennessee a plea before a judge ever leads to a possible expungement is if the plea is not actually accepted by the court and a conviction is NOT entered. This main way that this can happen is with a plea that is entered under Tennessee Code Annoated 40-35-313, also called judicial diversion. 40-35-313 experessly excludes DUI from the crimes eligible for a diversion plea. Reckless endangerment is not excluded but I do not imagine that most prosecutors would agree to amend a charge from DUI to reckless endangerment and let the plea be under 40-35-313.