Does the fan stay running when it is on high or does the fan stop?
At the battery junction box under the hood there are several fusible links one of them power the high blower and it is likely the problem. you can try lightly pulling on these to tell if one is bad if you can not find it that way they will need to be checked for power on both sides to determine the bad one. They look much like the pic below,
It is possible still a relay but when I asked if the motor still runs when you switch the fan to high and the motor stops that means that the relay is switching so I would first check the fusible links and if you do not find any of them bad I would check the relay it is located on the right rear of the engine compartment pic below of the circuit.