One of you will need to delete the existing account, then migrate their data to the new account. To do this,
on the phone that will be moving to the new account, go to Settings>iCloud and turn all data that is syncing with iCloud (contacts, calendars, etc.) to Off. When prompted choose to keep the data on the iPhone. After everything is turned off, scroll to the bottom and tap Delete Account. (This will only delete the account from his phone, not from iCloud. The other phone will not be effected by this.) Next, set up a new iCloud account on this phone using a different Apple ID and turn iCloud data syncing for contacts, etc. back to On. When prompted, choose Merge. This will upload the data to this new account. At this point you will have two different iCloud accounts, one for each phone, with identical data on them.
You will then have to go to icloud.com on your computer and sign into each iCloud account separately and manually delete the each other's data from your account (such as deleting the other person's contacts from your account, and vice versa). These changes will be reflected on each phone. When finished you will have individual iCloud accounts with just your own data on them.
You can certainly elect to not turn on data syncing with iCloud. Just follow all the steps up to creating the new account and leave contacts, calendars, etc. set to Off. If you want to onluy use photo stream just turn that on and leave the rest off.
You will still have to delete your sister's contacts off your phone manually if you don't want them. You can delete them one by one on your phone. Alternatively, you can turn on syncing for contacts, upload them to your new iCloud account, then go to your account on icloud.com on your computer and delete her contacts, when finished, turn contacts syncing back to of,f and when prompted, choose to keep the contacts on your phone.