I would suggest you consult with an immigration attorney. They are skilled at working with issues as those you present here and will be best suited to provide you sound legal advise. If you do not have an attorney, your local bar association can probably refer you to a seasoned advocate in your area.
All the very best to you!
NOTE: This Answer does not constitute legal advice. Every case is fact specific. To render a legal opinion, an attorney must engage in a consultation with a prospective client and review any pertinent documents. This communication does not create an attorney-client relationship with Attorney Amy L. Wells or WELLS LAW OFFICE, INC.
Immigration can and does qualify theft and fraud crimes of moral terpitude, meaning it does not hold up to community standard of honesty and good morals. The fact that the DA filed a nolle pros does help you however. You should be working with an experienced immigration attorney who will help you navigate through this process. Good luck with everything.