How do I convince my school to allow me to double major?
You can convince your university to allow you to double major by showing then a plan for the courses that you will be taking in the next semesters, so they can see that you have already thought about the future, and that you're not one more lost and undecided person. Also, as you said that you love Math, I would like to ask if you had good grades on those Math courses that you took. If yes, try to get help from professors, as they can make the path for the double major approval easier for you since they usually have more influence than a second semester student.

Since you said that your university sees itself as a box (the student comes from high school, enters the box and four years later leaves with the degree), you must try to find a way to show them reasonably that your plans are feasible. More than that, your logical arguments and plans for the future must be well designed and articulated. Furthermore, as I said before, try to get help from professors that know you and your joy for learning Mathematics.

As a double major student that recently gave up to other people's dreams and now is following his dream of studying Math and Physics, I wish you all the luck with your plans!