At most schools, (this was the case at my son’s) students request recommendation letters during spring of Junior year or beginning of Senior year from two teachers who then give the letters to the Guidance Counseling department which keeps the letters on file and includes them with each college application.
Your two prior recommenders don’t need to “build” on their previous letters, the letters were supposed to be about you, not about Questbridge or Georgia Tech, and the next letter shouldn’t be about you as well, not MIT.
That being said, if your CS teacher is willing to write an absolutely extraordinary recommendation describing you as the most outstanding student they’ve ever come across, then by all means ask.