First, I'm not sure you could consider a party open to anyone in the class of one race (and their guests) to be a fully "private" party. Second, if that party is held in a hotel, restaurant, or other place of public accommodation, it may well be subject to the Civil Rights Act of 1964.
And I would again argue that the school is participating in this discrimination.
I'd be willing to bet the elected courts of both proms appear in school publications, and I'd be surprised if there weren't photos of them in the yearbook.
If these aren't really anything recognizable as proms, but only private parties, it'd be another story. But that's not what it sounds like. There is only one white prom queen, and one black prom queen. It'd be different if it was customary to have a prom queen at any of a number of different private prom parties.
It was by invitation, not just "come if you're white".