You really are asking two questions.
The first question is whether the state has to drop the charges if the police didn't read you your rights. In almost all cases the answer is "no." Police are only required to read you your rights if they are going to question you after you are under arrest. Most DUI questions occur before a person is under arrest. Even if they were required to read you your rights, and you prove it in a motion to suppress the evidence, the result is usually that the state can't use your statement against you, not a dismissal.
The second question is what should you do. You should get a lawyer - plain and simple. You should ask the court for a court appointed lawyer or public defender if you can't afford one. If you make too much money for a court appointed lawyer or public defender you should scrape together the money to hire a good DUI lawyer. A DUI is too complicated to do by yourself in almost all cases. The problems that will follow you from a DUI conviction will continue for years.
Your Miranda rights only arise after you have been placed in custody. For that reason, very seldom do the police give Miranda warings in a DUI case - they have already completed 99% of their investigation before the arrest takes place. And the state-administered blood or breath test that follows the arrest has been held not to be subject to Miranda protection, either.
But if you were questioned after arrest without Miranda, your answers can probably be suppressed. And in some states, Georgia, e.g., if you were asked to perform acts such as field sobriety tests AFTER arrest, they could be suppressed, also.
You ask, "what should I do?" You should do your homework and find a qualified DUI Defense lawyer to defend your case.
Miranda and your rights under Miranda only come into play if the prosecution attempts to use statements made while you were in custody against you. The information obtained at DUI stops are a subset of that and come under a case called Berkemer v McCarthy. That case says that the police can ask you a couple of general questions while interviewing you about suspected criminal activity.
So, if you were stopped on the side of the road and the police asked -- as they usually do -- a series of questions that concern drinking, sleeping, eating and health is it a custodial interrogation or a pre-custodial interview.
I say it's the latter and often argue against the admission of any statements because the cops interrogation exceeds the scope made permissible by Berkemer v McCarthy.
Edward J. Blum