Get a degree in clinical psychology. You'll learn that everyone basically shares the same thoughts of inadequacy, the same kinds of guilt and shame. And that these feelings don't really go away with "success," but they might lessen with conscious attention (therapy, coaching, etc.)

But even better: share your feelings with a group of your peers. You'll find that they can all relate, and that you're not alone. The antidote to shame is (healthy) vulnerability.