You will not be able to get a public defender until the court
assigns you one which should happen on your court date. You may not meet him or her until the next date. So what you do on your arraignment is to plead NOT guilty and ask the judge to appoint you a public defender. That is the only plea a defendant should ever make the first time he is asked in court, as he is presumed innocent under the law. A not guilty plea is the only one that keeps all of your rights open.
The lack of Miranda warnings does not invaliate an arrest. In fact, Miranda warnings aren't necessary until after an arrest has already been made and then only if the police interrogate you. Here, it appears that they may have as you have said that you cooperated with them. That was likely a mistake, particularly if you made any incriminating statements or signed a statement telling what happened. However, if you go to trial
on this case, your lawyer would be able to challenge the lack of Miranda warnings and the improper police conduct to try to keep the statement out of trial.
This offense is a felony and carries a state jail sentence
of 2, 3 or 4 years of prison. See link to PC 244)
If you make all of your court appearances and follow whatever instructions the court may give you, you should remain at liberty to fight these charges. But you very definitely will need a lawyer, and you don't want to talk about this incident any further with anyone except your lawyer. So again, the only thing you want to say at your arraignment is that you plead not guilty, that you are without the means to afford to hire a lawyer and that you will need the court to appoint you a public defender. Once you get one, your lawyer should know where to take this from there.