When the outside A/C unit cuts off the fan inside stays on. I tried changing the thermostat already. Do you think it is the fan relay? Is that on the circuit board?

Are yo sure that's the correct model #. Some of the sytems use a sequencer to time on and off the blower, some use the time delay in the control board and the real old ones just used a simple relay. All are capable of sticking closed, keeping the blower on.