There is a resistor that you can buy from Autozone or equivalent. It is a Fan Speed Control Resistor, and is located behind the glove box. It is simple to remove, the hardest part is disconnecting the wire harness. The part is like 25 bucks, and is sure to fix your problem.
There is a blower speed resistor in back of the glove box that plugs in. The "high" setting is a common failure. About $30 for the part. You have to drop the box to see it.