Is there a way to load my own GUI app without the rest of the GUI in Linux? It's something like running Winamp only, and practically turning your PC into a music player.
X-Windows has a kiosk mode that can be used to start an application, usually a web browser, as the only running app, and not loading the full window manager. I don't know that it will work with Winamp, but you could try (from the console):
startx /path/to/winamp --kiosk