Where does T'Challas sister learn science from

All of your assumptions are based on the idea that Wakanda somehow has no learning institutions of its own and that all of the best learning institutions are in the West. Within the Marvel Universe, that couldn't be farther from the truth. You wouldn't ask the same question of Tony Stark because the answer would be irrelevant. The real (and frankly obvious) answer for both Tony and Shuri is that they are geniuses who would have likely arrived at their level of knowledge and mastery over multiple fields regardless of where they were educated.

For a deep dive into the Wakandan culture, government, and its education system (which differs radically from its hyper-capitalist western counterparts in structure and pedagogical approach) see Ta-Nehisi Coates' lauded run on Black Panther and Roxane Gay and Yona Harvey's World of Wakanda.

In other words, go read a comic book.

Sincerely,
Death Man