I agree with Wesley that this is probably an error not relating to apex_mail, but rather to the network acl or something in the mailserver.
And FYI: you don't really need to log in to the internal workspace (and you won't always get access to it ...). You can also check the views APEX_MAIL_QUEUE (to see what is queued up) and APEX_MAIL_LOG (log with sent mails and/or error message). Eg:
SELECT * FROM apex_mail_log ORDER BY last_updated_on DESC