I got a DUI and a hit and run about a month ago.. I went into court yesterday and they said that they had no received any charges against me and that the sheriff had not filed it yet. It has been over a month.. is there a time that they have to submit the stuff to the court by?

You are entitled to a speedy trial, but that's only AFTER charges have been filed. Since you are not in jail, the prosecutor can take their time in building and filing a case.