Lying on resumes for job applications is probably the most NT thing of all that AS people do, the nearest they come to conforming to an entrenched NT practice. Nearly all resumes use lies of omission (leaving a sacking out) or commission (claiming experience that is more than strictly factual). So you are doing something that is a cultural norm. There are a number of good studies that demonstrate how commonplace this is.
What you did is minor compared to people who claim they have doctorates etc. Put this behind you now, learn from it,
and focus on your real strengths, talents, potential and aptitude. Play to your strengths, and clearly list what they really are. There are other jobs, other agencies, and though it isn't easy, I wish you all the best.