Does this necessarily have to use chrome? With chrome you have to set your whole computer to use the proxy, whereas with firefox it's super simple to just enter your IPort and start doing whatever.
Ignore this if you already know about deleting cookies.
You won't be hiding your ass if you don't delete cookies. It is still useless to switch proxy if you don't delete cookies. To hide your ass, this combination must be done in their order:
1) Delete cookies and safer if you delete for good all your browsing data, cache and history as well. (when you have done this, do NOT browse the email's website)
AND then you
2) Switch proxy or IP address.
EDIT: and one very important thing also is to make sure you use 'anonymous' proxy.