external domain emails not being sent.

[tru3prodigy]

This is my first time submitting a issue. please pardon if im wrong.
Im deployed on bluehost shared hosting. when i try email to ids of external domains such as gmail or yahoo, its showing as succesful dispatch but im never receiving the mail in my inbox. but im able to send the mail to accounts associated with the site domain. I have tried swiftmailer and php mailer seperately and both work seamlessly without any issues that too with the same smtp configuration and login credentials. Im lost on how to debug this issue.