If your job doesn't involve driving for the company then they can't legally discriminate against you for this conviction. Companies are required to have a bona fide occupational requirement (fancy term for "a good reason") before they can discriminate against you for something like that. Contact the EEOC (eeoc.gov if you are terminated for something that has nothing to do with your job.
How Can I Get A First Offense Dwi Conviction Off My Record? I Don't Want My Work To Find Out If They Do A Background Check. I Live In Virginia
I want my under age drinking off my public record I want to make it privet
You can also check with the city hall and/or the DMV and see if you can do an "expungement" on your DUI conviction. If the State allows this, your record will be sealed from employers but the DUI will be on record for police, government etc. Most people contact an attorney to have the expungement of records done.