Will everyone see the giant bulge in my pants?

Probably not. If you wear tight pants with a big visible lock on top, people might take notice. More than likely, you are far more conscious of it than they will be. I’d suggest a cage that points the penis downward and has an embedded lock mechanism to prevent noise and odd shapes under your pants. The Chinese ones are typically cheap so you may need to buy a few before you find the right fit for your particular apparatus and clothing style.