It boils my blood to see a school administration so blatantly and wrongly take advantage of a student that they claim to be educating and preparing for the future. If anything, the administration should be in full support of the OP. If the OP can tolerate the pushback, and there is nothing in his school's policies forbidding, he should pursue the app. Let the administration spin their wheels. They can't sue him. And if they tried, they would lose. It's just absurd.
(maybe we should all publish the app to prove the point)