Dumb question but.

Getting back to the OP, it is ILLEGAL to have more than license. That's one thing in common in EVERY STATE. Somehow some state DOT screwed up in not informing you to surrender your old car license (which, with having a CDL, is now an invalid license). You'd better contact your local DMV for information rather than relying on a bunch of random posters online for information. If you get caught with multiple licenses, they will ALL be invalidated, and you'll have to go to court, before you can even re-take your CDL test IF they allow you to get it back.

You need to take care of this issue NOW. Your CDL is you employment document, without which you are out of work. Protect it at all costs.