I think she should be allowed to run as prom king. I mean...it's prom...it's only high school. And...she was NOMINATED as prom king. So if a certain percentage of the student body would like to see her as their prom king, let it happen. The world will not end.
However, I do agree with Talyubittu that she is still a female. Maybe she identifies as being male, but...biologically she is female. Maybe not psychologically, but def. biologically. Her body is that of a female and will remain as such unless she gets some sort of procedure done to change all of her internal and external organs to those of a male. What she feels she is has no jurisdiction over what nature has made her (again, excluding the psychological aspect). For example, I truly feel in my heart of hearts that I am utterly and completely awesome...now, that doesn't necessarily mean I am, right? Because, biologically, I could just be a real douche-bag and have over-confidence issues. lol, just kidding, bad example I know. But in all seriousness, don't tear me apart for this, it's just my opinion, so you kids can cool your jets!
Aside from all this, I still feel she is completely in her rights to run and win the title of prom king.