For my supermarket shopping my username is my email address.
Did you use your email address as username or did you have a name as your username for the shopping?
eg.
[email protected]. or galasalmon
Is it your details for the shopping or the details for your second email?
There will be a forgotten password option for both - the supermarket one will send an email to the email address you signed up to them with, Yahoo will ask you for answers to security questions or perhaps send a link to any email address you specified as a recovery.
Have you tried doing forgotten password with yor original shooping site details?