When I turn on my Central Air, I blow a 3amp fuse on my central air/furnace panel. When I replace the fuse, my fan will work as well as the heater, but when I switch it to Cooling again, it immediately blows the fuse, I've been through three fuses to figure this out so far. My question is where do I go from here,

Problem is likely with the low voltage control wires that go from tha Air Handler to the Outside compressor unit. Several ways to test.
The 2 wires send 24 volts to the compressor contactors coil for cooling.
You either have a short on those 2 wires(eleminate short), or the Compressor Contactor has a shorted coil(replace contactor).
Good Luck