"He never read me my miranda rights,"
He isn't required to. Anything you said prior to being arrested was a voluntary statement on your part and they can use it at trial. The cops are allowed to take advantage of your honesty and inability to remain silent. You obviously know what Miranda is and didn't exersize your right to not make any statement. FYI: Miranda is ONLY required if you are in detained custody being questioned AND they want to use the statement at trial. In your case even if your statement was suppressed they have the officer's testimony that you smelled of alcohol and appeared intoxicated. In many states that is enough to convict. Especially since many DUI defendants refused the blow.
"I passed the breathilzer test and no urine or blood test was done for drugs."
They aren't required to do blood or urine. All the prosecutor needs is your admission that you took the prescription tranquilizer and had a drink combined with it.
"can the case be thrown out"
Doubtful. They have your confession. At best you can hope for them to downgrade the charge to something lower than DUI since you passed the breathalyzer.
"Any suggestion would greatly be appreciated"
Listen to your attorney. Unfortunately you WERE driving under the influence. It doesn't matter that you are on the lowest dose of Xanax it is a tranquilizer that is 150 times more powerful than Valium. Just driving with that in your system alone is enough to trigger a DUI arrest. Yours was combined with a hard alcohol drink.