Right now is too late for any plan adjustment, so just have to wait.
There is no reason one has to follow private school STEM schedule. One can even self-pace AP Calculus doing Khan or any on line math self-help so long as to register and take the College Board AP Calculus tests. Many private schools lack the resources of public ISDs so it is common for them to be behind.
The preferred schedule to be good (or surviving?) TAMU engineering is Algebra I at 8th, Algebra II/Geometry at 9th, pre-Cal at 10th, Calculus BC (not AB) at 11th. Differential Equation and/or Discrete Math at 12th. Even completing this series, actual classes rigor at TAMU are still much tougher as professors are not inclined to explain steps in detail (TAs do, but they are not paid high enough to help hundreds of students).
The tough math requirement at TAMU has its reasons, students scoring 4s or 5s in AP Calculus BC can still tank their Calculus III and Diff Eq. And majors like MEEN, AERO, BMEN and CHEN can easily have over 40-60 hours of classes requiring Applied Calculus. The learning curve will be very steep for those with pre-cal only. TAMU does have Math150 for those with pre-cal but a few months proved to be hard for students to catch up and they are planning to move away from that model.