Will a 13 Year old Expunged Felony Conviction prevent me from getting a job with the U.S. Postal Service?

Long story short....Thirteen years ago, I was a bank teller and was blamed for cashing a check for a customer on an account that wasn't hers. The bank blamed me for it, and pressed charges, even though a total stranger was the one that cashed the check and left the bank with the money. I was a single mother, couldn't afford an attorney, had to use a public defender, who told me that I would go to jail for 5-10 years if I didn't plead guilty. Another long story short, he told me that I would be able to have it Expunged after the case was over. I thought Expunged meant ERASED, and BOY was I wrong. I never went to jail, was ordered probation, but it was cancelled immediately, they just wanted to convict SOMEBODY, and I was responsible. I am now seeking employment and have registered with an agency in the Dallas area. They REALLY want me to go and interview with the US Post Office. It's EXCELLENT money, but they require Security Clearance!! I haven't had any problems getting other jobs, but I also haven't been fingerprinted for any other jobs. I have had regular criminal background checks, but nothing shows up. Should I even bother applying? They (Post Office) ask if I have had any convictions in the past 7 years, and I had and have NEVER been in trouble except for that. Should I save myself the embarrment at my agency?