What can I do if i'm trying to get a tax refund and my account number is 20 digits long, and I'm not able to write it all down since turbotax has a digit limit?

Bank routing numbers and bank account numbers are nine digits.  So you have something wrong.   Check with your bank and verify those numbers with them before you try to enter banking information for your refund.

But on the turbotax page it says that the checking account number is usually 10-12 digits, meaning it does not necessarily have to be exactly 9 digits and it also allows you to enter up to 17 digits in the account number field

Please call your bank and ask them.