I know they were forcing everyone to switch to a Yahoo! email address for a while there, then they relented and let you use other email addresses again. But this sounds more like someone hacked your email account and used it to change the password OR that someone has tricked you into clicking on a page that LOOKS a lot like a real Flickr/Yahoo! Page, but isn’t.
Might want to change your email password as well, just in case. Don’t click on any links inside of emails or on pages that another page sent you to (i.e., if “Flickr” sends you to Yahoo!) and make sure the URL has the lock icon, preferably a green one (for extended validation).
Best of luck.
—Patrick
