Nike-Running App

If you are getting the option to 'open' the app in the app store then that implies that it's already installed on your phone.

If tapping on 'open' doesn't open it then does it show on your phone's multitasking bar ? If it does then try closing it from there : double-click the home button to open the multitasking bar, and if that app shows there then swipe or drag the app's screen from there up and off the top of the screen to close it, and click the home button to close the taskbar.

Then do a soft-reset : press and hold both the sleep and home buttons for about 10 to 15 seconds (ignore the red slider), after which the Apple logo should appear - you won't lose any content, it's the equivalent of a reboot.

When the phone has restarted see if you can find it on any of your phone's homescreens (you can also pull down the centre of your phone's screen, not from the very top, to reveal a search field at the top of the screen which you can use for searching the phone), and/or whether it then has the cloud icon against it in the store for downloading.