Obligatory Prayers have obligatory conditions including standing steadily facing the Qibla which is not possible during driving. If the time of the obligatory Prayer is going away, you must stop driving and perform your Prayer with its obligatory conditions, then continue your journey.
Recommended Prayers can be performed while driving or walking or traveling.
There is no problem with that.
May you always be successful
Muslim woman can request a female examiner to avoid showing her ears to non Mahram men.