I filed with Turbo Tax last year and I can't access my account. It seems my recovery information is being sent to a different e-mail.

Yes, there are other ways to access your account. Try this alternative where you can  get help signing into your account by entering your phone number. 

Click on the link for the steps to change your email address.

I got an e-mail saying my account was accessed in August 2019 and it wasn't me

Yes that is correct

If your verification code is being sent to an email you no longer have access to when trying to recover your account, I have provided a link below that may be able to assist you:

Get a verification code if the email address is incorrect