Family Sharing does not share accounts, it only shares storage. You should already be using your iCloud account with Family Sharing.
As such, getting your own subscription to iCloud storage would not in any way affect your data as long as the process is done correctly.
You subscribe to iCloud Storage yourself on your own account, and then leave the Family Sharing group. Your data will remain un touched and safely stored.
If you are by any chance sharing an iCloud account, which should absolutely not be done, then you will need to download all your data form iCloud, and then copy it into a different iCloud account you wish to now use.
Then you can also subscribe on that account to more storage on your own if you require.