No, your CS5.5 key will not work in version CS6. You'd have to purchase a CS6 upgrade to get a CS6 serial number.
Bear in mind that with Adobe's new one-version-back policy, you must upgrade to CS6 if you wish to enjoy future upgrade pricing to CS7 and beyond.
To get CS5.5 again, you should be able to log in to your Adobe.com account at the Adobe website and retrieve your download from the My Orders link.
Failing that, you can download CS5.5 from http://prodesigntools.com/adobe-cs5-5-direct-download-links.html
Ensure that you follow the Very Important Instructions (steps 0 to 6) on that page first otherwise the links won't work.