[kazinator]

It sounds like you have fallen into something that is nowadays referred to as "impostor syndrome". This is when people who are competent in their field underestimate themselves: they harbor as suspicion that they are actually not competent and think that others around them have somehow been duped, perhaps only temporarily so.

Obligatory Wikipedia link: http://en.wikipedia.org/wiki/Impostor_syndrome

It may help you to remember that if you actually were an idiot, you'd likely be the opposite way: irrationally confident in your abilities. :)