Anyone can create their own blockchain, but you will not be able to reconcile your chain with the bitcoin blockchain at a later date (even if you start your chain by forking off from a certain btc blockchain block height).
I don't know what your use case is, but if you're not going to use an already existing blockchain, I would expect that creating a private database (SQL?) would be a better choice than trying to create a private blockchain.
You could, for example, create a database that is designed to mimic the balances of bitcoin addresses you control. Users of your database could freely transfer these 'bitcoins' to eachother on your server, and then only when the user wants to move value to someone outside of your internal system, would you need to initiate an actual bitcoin network transaction.
So the actual bitcoin you control would function as a 'reserve' that your database's value is backed by. This is basically how centralized exchange services work. The users of your system will need to trust you in using it.