Class C misdemeanor and a Job

[Pierre]

I'm a recent college graduate and a year ago I was convicted of a class c misdemeanor which was actually a plea down. See I was leaving campus and my lights were off. A campus police officer stopped me off campus. I had my fire arm in my car. I told him i had my fire are in my car plus it was registered in my name. He took me to jail anyway. Aside from two speeding tickets this was my first offense. It was a felony but they did me a "favor" and brought it down to a disorderly conduct charge which is still on my recored. I've been having trouble finding a job in Ky. I'm moving to NY and I'm wondering will this show up on a background check even if I get a New York drivers license? And also will this prevent me from getting a good job? If so I feel like I've wasted my time in college..