I suggest you hire a lawyer who has experience dealing with colleges (or whatever level you are in) and matters of alleged academic dishonesty.
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Carefully read the procedures and rules for the Academic Integrity Board, and comply exactly with all provisions -- particularly deadlines and time limits. Failure to do so can constitute a waiver or forfeiture of your rights to appeal the professor's determination.
Each school's administrative appeal process is distinct, but there are some broad commonalities. In most schools, you are entitled to the time and opportunity to retain and consult legal counsel, and you should do that. Most schools will not allow an attorney to participate in your appeal hearing (and some will not allow your attorney even to attend), but an attorney can give you meaningful assistance in identifying and gathering relevant evidence and in raising substantive and procedural objections to the fairness of the process.
In candor, no matter what the formal description and provisions of the admin appeal process, many schools disregard or revise ad hoc the provisions of the process as it suits them, on the justification that only "substantial" fairness is required. Students often find that their "rights" are whatever the school is allowing that day on that case. Don't expect that this these process will be fair or honorably conducted. Students don't often prevail in these appeals.
Public schools are a little bit more predictable and careful in honoring students' rights to a fair process. In private colleges, the school will do what it wants, no matter how unfair or inconsistent with the school's own rules. Private colleges are fiefdoms.
But the merits and integrity of these processes aside, students must rely on the published process because there is no right to sue in court instead. Even after exhaustion of the admin process, in most cases there will not be a legal basis for suit, and courts honor the tradition of "hands off" of school affairs to a degree that shocks attorneys in other practice areas.
I have seen school disciplinary cases where: the accused was not allowed to attend the hearing; student was never given a statement of the alleged misconduct; "Student Court" refused to look at the student's defense evidence; the identity of the accusing person was kept secret, along with the evidence of the accuser's mental instability and widely-known malice toward the expelled student; the co-habitant of an accusing complainant served on the adjudicating "Board" to determine the truth of the accusation. The results of the schools' lack of respect for any principled or ethical fact-finding process are often tragic and life-changing for the accused victim.
You should already know the consequences that can ensue if the AIB finds against you: dismissal; ineligibility for admission to other schools; 2 year shut out for some student financial aid; potential acceleration of repayment obligations of some current student debt; ineligibility for internships, externships, military, athletics, and educational abroad programs sponsored or partnered by your school; state licensing and employment disqualifications, forfeiture of earned course credits; forfeiture of tuition for current term; freezing of your transcript; etc.
You will hear through the grapevine that you can sue -- for defamation, breach of contract, deprivation of civil rights, infliction of emotional distress, etc., but don't get distracted by the idea that the best defense is an offense. There have been just a handful of successful cases by disciplined students in the whole country over the past 20 or so years, and all of those suits cost the student and family more than was eventually recovered, and none of those suits undid the damage and stigma of being labelled a cheat by the university.
In all events, you should consult with a specifically-experienced attorney in your area, perhaps one who is well-known to the college and active in its alumni or fund-raising affairs. Spare no effort here. Make the very best defense that you possibly can. You are in a war.
I wish you success.
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