First, you should not admit that you are guilty - it is the state's burden to prove that. Second, you should post this question in Maine to get the most accurate answer.
That being said, I handled a similar matter for a Massachusetts resident who had an unpaid parking ticket from when he had gone to college in Maine that resulted in his right to operate in Maine being revoked. He had a valid license in Massachusetts and when on vacation in Maine he was pulled over for speeding and the old suspension came up. The prosecutor handling the case was willing to dismiss the charges without his presence in Court once we produced documentation to demonstrate that he had taken care of the old ticket and new ticket and that he had made a donation to a Maine based charity in the amount of $150 in lieu of court costs. You should contact a local attorney who practices in the Court in which your case is pending to see if there are any alternative dispositions such as the one I referenced above, which might be available to you.
Disclaimer: This answer is provided for informational purposes only and it is not intended as legal advice. Additionally, this answer does not create an attorney-client relationship. If you wish to obtain legal advice specific to your case, please consult with a local attorney.
You should contact a lawyer immediately. If the prosecutor is not willing to dismiss, you may be able to get it continued without a finding if you pay the to tickets. That should not come up in a Cori check.
Mr. Thomas is licensed to practice law in Massachusetts. This response is not legal advice and does not create an attorney/client relationship. This response is in the form of legal education and is intended to provide general information about the matter within the question. Often, the question does not include significant and important facts and timelines that, if known, could significantly change the reply. Mr. Thomas strongly advises the questioner to confer with an attorney to make sure he or she gets all relevant information to make informed decisions about the subject matter.