It is hard to say from the question which type of lawyer you should consult with, because there are different specialties which might apply. For example, do you have any sort of disability? If so, you may want to consult with a lawyer who practices disability law. Do you have any reason to believe there may have been discrimination based on your being a member of a protected class, such as discrimination based on gender, race, national origin, sexual orientation, etc. If so, you may want to consult with a lawyer who handles such discrimination complaints. If you believe that the school violated its obligations under your student handbook, you might want to contact a lawyer who handles contract disputes. You could also consult with somebody who specializes in civil litigation. In my practice, I handle all sorts of educational issues. I don't know enough about your case to know whether it is something I can help with, but if you would like to set up a consultation, please feel free to contact me. At the very least, I might be able to steer you toward the appropriate specialty area.
Attorneys widely experienced and skilled in student (university and college) disciplinary matters and in appeals of university and graduate level dismissals and expulsions are practitioners of administrative law. You want an admin law attorney who has specific experience in university discipline matters, hopefully one who has prior experience with your university (an enormous advantage). This is a very specialized niche of legal practice and a lot of the procedures and rules are very counter-intuitive, even for general litigation attorneys.
For example, very few universities and colleges allow an attorney to participate or even attend the "fair hearing" meeting that follows your notice to the school of an appeal of a decision of dismissal or order of expulsion. So, the school appeal process somewhat resembles grand jury proceedings where the student must repeatedly exit the room and obtain legal advice in issue-specific nuggets throughout and over the course of the meeting. Further, it is typical in school administrative law for the period of appeal of a dismissal or expulsion to be very short -- as little as 5 business days in some cases. I cannot really make a sense of the procedure that you describe on these abbreviated facts, but I hope that you are still considered timely in your appeal of the school action.
School disciplinary processes are a law unto themselves substantively as well as procedurally. Schools have enormous latitude to design their disciplinary and fact-finding processes and they are given extreme deference in factual findings that relate to academic performance, graduation and degree standards, and quality of student work and conduct. There are many very extreme and heart-breaking cases of student discipline that could not have resulted as they did if the cases had been heard in civil or criminal legal processes.
Good luck to you.
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