Run CB Radio from AUX power
You should be able to run the radio from your car.

The "12V" supply in a car is not very well controlled. It is just whatever the battery voltage is. When the car is running and the alternator is charging the battery it can be up to 14V. Given that 13.8V is often stated as the charging voltage for a car battery, I would assume that the 13.8V input is actually a "power from a car" input, and will happily take whatever the car is actually putting out.