Hello and welcome to Just answer.com, Super mechanic here. About your vehicle.
It sounds like the compressor pump motor is drawing too much current, or is shorting out. You will want to try it with the connector unplugged to see if the fuse will not blow. The relay is internal with the compressor assembly.
Here is where it is along with a diagram of the circuit.
Master technician
29 yrs. exp., ASE master, cert. in G.M. electrical, a/c, susspension, brakes, electronic steering