First solo job on my car didn't go so well .... Aaarrrrggghhhh!

Take the tools your mom trained you with. If the heels don't work, use the butter knife.

Exactly.

Sounds like its leaking from the joint between the core and the tank. A pressure test should have showed that at the radiator shop, especially since you didn't even pressurize the system before it started leaking.

Sounds like the radiator shop skipped a step.