In most states in the union a cocaine or narcotic DUI is the same as an alcohol related DUI, except with a drug DUI, the DMV may not suspend your license under the "implied consent" laws, which means if your alcohol level is, e.g., .08 or above, the DMV can suspend your license even if you are found not guilty or the district attorney doesn't press charges against you.
But it is important that you continue with the rehab to demonstrate you are responsible and it is very important to know that to detect narcotic impairment, takes special training and most cops don't have this training. It isn't like detecting alcohol, because everybody knows what being "under the influence" is.
Also important is don't talk about this case with anybody except your attorney. Another relevant aspect of DUI cases is that the police must have a valid reason for detaining you to justify their arrest. It pertains to your Fourth Amendment right to be free from unreasonable searches and seizures, which includes arrests.
I hope this information is helpful.