well i hate to say it, but usually when this happens it is because the SWR meter is not being used correctly, and you don't notice that you have a direct short from the whip of your antenna to the vehicle body.
that being said, CB is pretty dead these days and depending on where you live, you may or may not hear anyone on any channel for days on end.
first, we need to know the details of your installation. the better info you give, the better help you get.
how and where is the antenna mounted?
be very specific with what you used to mount it, and any problems you ran into in doing it.
next, are you sure you know how to properly use an SWR meter?
when the SWR meter is in the CAL position, and you key the mic, does the needle move over to the far right side of the meter?
can you set it to the CAL position using the pot on the meter?
do yourself a favor and google how to use an SWR meter and check your techniques.
one simple test you can do right now is to go out to the car, unscrew the antenna from the back of the radio, turn the radio on, and turn the RF gain all the way up (this should always be set at max, and you won't hear anything out of your radio if its set too low), then turn the squelch all the way down (this should be left in this position otherwise you will not hear weak stations), then turn the volume all the way up.
make a mental note of how loud the hiss coming out of the radio is.
now screw the antenna coax back into the radio with the radio still on.
did the increase in noise startle you? that is good.
did you not notice any change in the receive sound when you plugged the antenna in?
that is bad.
you may still have a mic problem or some other problem, but let's start with what i posted.
again, be specific and we can probably get this solved.
LC