Take a look at the sentence again:
In preparation for the quiz, La'Mia studied comma splices and fused sentences
until she thought her brain would burst, finally,
she put away her notes, convinced that she would remember the rules even
on her death bed.
The problem occurs between burst and finally. La'Mia studied comma splices and fused sentences ... begins a complete sentence. Finally, she put away her notes ... starts the next complete sentence. Because these two parts have just a comma between them, they create a comma splice, a major sentence error.
To fix the problem, you could put a period after burst and then capitalize the F for finally.