Board Game Arena

Can I create my own game, whiteout share whit everyone?

If yes, I'll try something
If no, well I guess I wait.

Yes, you can. By default new projects are visible to everyone, but you can change the visibility any time you want on the control panel of your project.
The project I'm working on is not visible (not my choice though, I'm not the original coder on it and BGA admin have asked me to keep it private).