The short answer
Yes, you can carry on working with your own car, as long as the vehicle really is yours and you are the one driving it. What the new law set out to ban is something else: the use of loan-for-use and usufruct contracts to put cars into the activity that do not belong to whoever drives them. This is the so-called slots problem, cars registered in third parties' names and passed from driver to driver.
Article 12 of the revised regime bans loan-for-use and usufruct contracts for assigning vehicles to TVDE activity. It then opens a single exception, and that exception was designed precisely to protect people who work with the car they bought.