If you don't cancel before the end of the trial, Adobe automatically charges you using the payment information you provided when you subscribed for the trial. This information applies to the trial you set up using your personal account, not your student account.
I can't advise you on what to do about the student account. You could try opening Creative Cloud, logging out of your personal account, and then logging back in using your student email. If that doesn't work you will need to talk to your educational institution.
Note that the COVID-19 support for educational institutions is not an unlimited term of access. Adobe is providing "free" access to its Creative Cloud apps only if you are in education as a teacher or student. For institutions that give students access to Creative Cloud apps through on-campus computer labs, Adobe is enabling those students to work remotely through May 31, 2020, through a temporary "at home" access. This has to be set up through the school.
If you need to talk to customer support to get your trial canceled, be aware that because of the pandemic, wait times are far longer than usual due to reduced staff and higher demand. Please be patient with the people to whom you speak. Like you, they are feeling a great deal of stress. A little patience and understanding will go a long way to helping you in your particular situation.
Trials usually run for 7 days and they will automatically switch into a paid subscription once the period is over, so please make sure to cancel in time. Should you miss the cancel date, don't worry: If you cancel the (now paid) subscription within 14 days, you will receive a full refund.