Should we install CiviCRM again and import cleaned up data?
By "new account" I assume you mean a new CiviCRM instance (a new install). 

If yes, then yes! You can start fresh in a new CiviCRM and import the cleaned up data. If you search for "CiviCRM Import" you'll get a number of useful search results related to importing data, including tutorials. 

But if you have a complicated data structure you may be better of trying to clean it up in the existing instance.