The public defender IS an attorney. Either a public or a qualified private attorney will do. Normally you must be brought before a magistrate within 48 hours of an arrest (Saturdays, Sundays and holidays excepted) on new charges. In your case you are also being held on the probation violations which do not carry with them a speedy trial right. I do not know why you were not arraigned promptly on the new charges but it could have to do with the no bail warrant from the county where you violated your probation.
I would definitely suggest hiring private counsel. You are looking at penalties for the probation violation and for the new case. If you hire an attorney, you will give yourself the best chance of having these penalties run concurrently (in essence, only receiving one punishment for both).