let's bring order into your question. I guess you upgraded from CS (Creative Suite) 5.5 to CS 6. Usually when you upgrade to a newer version its no problem to open older files. The error you got points me to the assumption that the files were saved with a newer Version of CS6 (than try if there are any updates für CS6) or with InDesign CC (Creative Cloud). The only way to open the documents is to save an IDML file with the newer version of InDesign.
If its the way you described, than reinstall CS6 and try again. When you have CS5.5 still on you machine please try to open a file and save it as IDML.
I'm curious if any of my guesses was the right one.
What is the FULL error message?