It is possible to use the 2020 books to take a test in 2021 for AAPC. Some proctors may not allow it, but it is the test-takers option. The answer may not be accurate for some questions.
To update your 2020 book with the 2021 code changes, you can pencil them in. Do NOT glue or tape any information as you will be required to pull those off your page. This may be a daunting task however to write all the new codes. Plus directions for proctors indicate notations required for daily work can be include but not lengthy content.
Can you borrow a 2021 book from someone? There is nothing on AAPC that indicates you cannot bring 2 books - one of each year. The 2020 with your notes and the 2021 you borrowed may be something to consider. If that is the case, I would notify your proctor ahead of time to let them know you intend to bring two copies. Personally, I would allow it as a proctor; but everyone is different.
And I am not sure if you are doing the online exam what they do with two manuals. If that is the option, I would call AAPC if you are doing the online exam.