The only way I know about using the right Shift key as a shortcut by itself is in System Preferences, Mission Control. There you can define shortcuts for Mission Control Application Windows, Show Desktop and Show Dashboard.
None of them let you go to the App Switcher, which seems to be what you ask when you say "Show apps that are open" – but maybe not. Maybe you just mean Application Windows?
The shortcut to get up App Switcher is pretty standard: Command + Tab. Although you can change it to the right Shift key, it would not make sense because you need both a modifier key (Command) and a key to press to move on to the next app (Tab) for it to work.