In addition to potential punishment for the new crime of filing a false report, if convicted on the new case, you would be in violation of your probation on the DUI. One of the standard terms of probation is to violate no laws. Potentially, additional jail time could be imposed for the violation.
How do you get an extension if you need a lawyer? Either you can find an attorney before your next court date or when you appear, ask to continue your arraignment so you can hire an attorney and have them appear with you. Since you're on probation, the court technically could take you into custody and hold you pending a probation violation hearing. That is unlikely, but a possibility. If you have time before your arraignment on the new case and are looking to hire an attorney, I'd do it soon.