The prison Governor is part of the administrative arm of government so what you describe as a “prison adjudication” is an administrative tribunal not a judicial court. From you description, it appears you have a dispute with or within the prison and this procedure has been offered to resolve it. No doubt there is an underpinning law that allows the government, through the Governor, to make this decision. There may also be an appeals process within the prison system that can follow it.
This is all perfectly normal and legitimate and is a common way for government to ensure it makes its decisions fairly.
The courts will not get involved unless and until all the administrative avenues have been exhausted. Even then, the grounds for appeal to the courts are limited to “the government didn’t follow its own rules” and not “I don’t like the decision I got”. Government officials, like prison Governor’s, have discretion to make decisions and courts will not interfere with those decisions, even when they are wrong, unless the decision making process didn’t follow the rules for making decisions.
It’s similar to the way football referees can mistake a goal for no goal or miss an offside. They can make mistakes. However, if they are taking bribes to make those “mistakes” ...