Sounds like wires were hooked up wrong when you screwed up the switches & you created a short. The popping sound was a relay, fuse, or resistor going ... no way to tell which without seeing the wire diagram and knowing which wires you connected to the wrong switch.
Best approach (IMO) would be to get the wire diagram and specs on each component from the shop manual. Using a multimeter, first, trace power from battery/keyed hot through the circuit. That'll tell you if a switch, relay, fuse, fusible link is fried. A test light will tell you if power is getting there, but the MM will also give you the voltage (drop), which might help find corroded connectors. Then, check internal resistance on the components and connections against specs to see what else you may have damaged/burnt (fan resistors).
As far as chafed wires/harness shorts, etc. ... trace the wires. If you were working, you could jiggle the harness at various spots to narrow down the area to open based on being able to shut it off by moving the wires. A powerprobe might help narrow the direction of search. But not useful unless you get over the learning curve or you could create shorts with it.
Don't open the harness until you are positive that you are/are not getting power to ( and through) the components that need it -- switches, relays, fan motor, etc. If you have power, disappear between two components (hot at switch out, but nothing at relay in or hot at relay in/nothing at relay out) the short is in that segment of wire or that component.
Double check ALL your fuses for continuity before starting, AND make sure all your switches are wired correctly, or you'll never figure it out since you'll be reshorting every time you apply power.
It's always a good idea to fix one thing at a time, then decide if you need to do more. Start simple (cheap) and work toward complicated (expensive). Throwing parts at a problem is usually an act of desperation, and if the fuses are working as intended, the parts may be fine, even with a short. Finally, once you have it fixed, a bit of dielectric grease on your connections goes a long way to avoiding corrosion related voltage drop problems in the future.
When you are sure that you have power going where it needs to, you still need to evacuate and recharge your a/c lines to get it to cool, since you opened things up when you replaced the compressor. Evacuating is vital to get the moisture out, or you'll be doing this again in July.
Good luck.