Is there a word for irrational doubt or lack of confidence?
If the doubt is irrational, then it’s imposter syndrome:
Impostor syndrome is a psychological pattern in which one doubts one's accomplishments and has a persistent internalized fear of being exposed as a "fraud".
This phrase can be directly inserted into your example sentence.
If there’s not an element of accomplishment involved I would just say it’s just low self-esteem.