The 3A fuse in my Air Handler blows

Well, there has to be a short some where. First check the stat cable outside where it comes from the house to the outside unit.

Without a meter, fuses can used to troubleshoot. Replace fuse and try just Fan, if it doesn't blow fuse, Try heat. That engages Heat and Blower. If it doesn't blow, it is likely the wiring to outside compressor. Try Cool, If it blows, as mentioned above and is most likely culprit. Could be either the low voltage control wiring to compressor, or shorted windings on the Compressor Contactor Coil. Follow wires and look visually for any shorts. Many ways to trouble shoot from here. Disconnect wires at contactor and try again. With a meter you can verify no short on control wires or a shorted coil.
Good Luck