Having a false sense of self is like most things imo takes constant and often proper thinking to adjust. I had some similar feelings when I received my bachelor degree.. like I didn't really earn it (it felt too easy) and maybe I didn't belong doing and trying to continue in a career. I think it was the overwhelming stress... the expectations of others (or what I perceived them to be)... getting to me.
We have to realize we are entitled to whatever we can accomplish. As human beings... this is the human being experience, this is what we do!