Hey yuki_kim,
Sorry to hear there's been some difficulty linking your Steam and EA accounts.
I'm afraid we're unable to directly support account-related requests like yours here on the forums, as we don't have the right tools or records. Contacting our support team as you have is the best way to proceed.
Seeing as the message implies the Steam Account is already connected to an EA account, it may be worth trying different login methods to make sure you're using the right EA account. A 'ghost' account is at times created when you log in using a different method (e.g., sign in with password instead of signing in with Google). There's a chance that your Steam account is linked to that other account.
Please give that a try and let us know how it goes. Thanks!