Update: Finally I reinstalled everything without the ID and is working just fine, I'll use my personal Apple ID to download Xcode and I'm never going to create a new one again.. Thank you so much for your comments!
Final update: I feel like a complete idiot. As @tobiasbischoff said, a simple user swap could resolve all of this.. I hope tomorrow I can recover my lost IQ from today! ahhahaha.
I thought there was a quick, scriptable command-line method of downloading xcode: