heater blower won't shut off on 1998 Chevrolet Cavalier

My blower runs on the passenger side and will not shut off until I turn of the car. When accelerating it will shut off until I get the car in gear (it's an automatic) and then starts again. The defrosters work but not at full power and heat comes out of the other middle vents as well. Could this be the blower motor resistor?
Thank you for any help you can give me.

Asked by for the 1998 Chevrolet Cavalier