I recently installed InDesign CC. Now I can't open my files that were saved in CS6. The pop up says the files are damaged.
Do you still have InDesign CS6 installed (as well as CC2014/2015?)
Try opening in CS6 and saving as an IDML and see if it will open in CC.
Troubleshooting 101: Export to .idml or .inx to clear file corruption
Retrieving data ...