I'm a Psychology graduate and I'm currently a software engineer. I used to question whether I'm good enough to be in this position as I'm a graduate of a different degree and I work with professionals who are CS graduates and have certifications. There used to be times when impostor syndrome hits so hard it becomes mildly depressing. I still experience it at times.
One of the things that helped me push past this syndrome is recognizing I have it. Just being aware of it means you can do something about it. You can try to deal with the root cause or the symptoms themselves and see which one works for you.
Another is reading the testimonies of accomplished developers about their experiences about impostor syndrome. I read somewhere that one of the developers of Twitter Bootstrap didn't know what he was doing in the beginning. It was pretty uplifting to know that there are others like me and those others are sometimes actually pretty accomplished.
I think the better you get at your craft, the more you realize there is so much you don't know. So it's a good step to look back to see what you've done so far -- how far you've come. After that, look ahead with excitement towards the things you would like to accomplish. :D
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