I cannot be to precise since your question fails to identify the area of your dispute. However, in most administrative hearings the hearing officer is acting on behalf of the agency and he makes a recommendation to the agency. You have the right to request a rehearing by the hearing officer or to appeal to the agency citing the hearing officer's errors. If you fail to exhaust these administrative remedies you are going to have a difficult time convincing a writ court to help you. Once the agency affirms the hearing officer's decision your remedy is to file a petition for administrative mandamus in the Superior Court. There are pro bono organizations that may be able to help you. Many law schools also have clinics that might be a source for help. Good luck.

The degree of formality in an administrative hearing differs between departments and agencies. Some, like the Employment folks, are quite informal and just have a hearing officer sit at a conference table with the parties and their attorneys. Others, e.g. the Public Utilities Commission, sometimes have black-robed administrative law judges and more of a courtroom atmosphere, often with a reporter taking minutes.

It would be interesting to know the rule cited, so we could check into whether it followed regulation, didn't need to follow for some reason, or was sufficiently off-base to serve as a basis for appeal. Sometimes hearing officers and ALJs may cite rules that are valid and pertinent, even though not to be found in the rules of procedure or administrative code. At other times, they may make up stuff to bring the hearing to a close by quitting time.

If (or when) you receive a written decision from the hearing, it may include instructions regarding appeal. I would tend to think you need to follow these, particularly with respect to timing and deadlines.