First of all, free advise is worth exactly what you pay for it....nothing. Yes, get yourself a lawyer.
Second, you cannot plead guilty to a crime you didn't commit. A Judge has to hear you admit you did the things the police say you did. If you say, "Judge, I didn't do it, but am pleading to make it just go away", he can't accept it. Plea bargins are for people pleading to a lesser, included offense, not for innocent people. If you plead guilty, you will have to admit you did what the police charged.
Miranda is only an issue if you answered questions about the crime. Miranda isn't required to just ask you name, address, and other identifiers. So if they just asked you for your identification and wrote you a citation, they weren't obligated to Mirandize you.
The law and rules of evidence vary from state to state, so don't believe something someone (including me) outside of California tells you.
Good Luck
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