I canceled my license on Adobe and re-registered my personal account with my student number email address.However, I am unable to use the applications allowed by the university.

You said you created your personal account with the student number email, but that is not a problem in itself.
Please try logging in again.
※All you have to do is select your "Company or school account" as you will be given the option to log in.

Regarding whether you are logged in correctly, there is a method on the homepage of Center for Science Information to confirm that you have successfully logged in to Adobe ETLA.Please follow the procedure at the URL below and check it.

【How to check if you have logged in correctly with Adobe ETLA】
https://web.sic.shibaura-it.ac.jp/faqs/faq_questions/view/74/8a48e9cab1a63fcf8a4a1297bb4e6b5d?frame_id=163&lang=en