It could quite possibly be your power steering pump. I own an 03 Town & Country and the pump does whine quite a bit. I did change out the fluid and it reduced it but it still makes noise.
you may have a small leak some where to the power steering pump. if it is sucking in air then it will wine quite a bit. all it takes is a few air bubbles to do it. like a hydraulic pump if it gets a little water in the fluid it will lose alot of pressure.
If your power steering got low on fluid and got air in the system you will have to make sure its full of fluid and then turn the wheel both ways as far as it will go,if this doesn't fix the whine your pump bearing's are going bad and eventually will need replaced.They will run that way for a long time if you can stand the noise.