I have a 2006 cobalt, lock cylinder gets stuck, car will still turn on and off

My cobalt makes a beeping noise as if the car door is open when the key is out
of the ignition. The key will still turn off and on the car, but when I turn off the
car I can feel that it won't make that clicking noise, it gets stuck, which is
causing that noise as if the door is open with the key in the ignition, but the key
is not. How could I fix it, do I have to replace the ignition?