More than likely your blogs are already being stored in separate databases. As you probably already have installed two copies of your CMS (Content Management System) of choice, one in your main domain's directory, and one in your add-on domain's directory.
If this isn't the case, and they are both currently storing to the same database for some reason. Depending on the CMS you are using, you'd typically need to install a fresh copy for your personal blog, export the data from your shared database, and then import it into the new separate one.
In order for us to better assist with this question, if you could please let us know what CMS you're currently using, and if you login to cPanel and under the Databases section click on MySQL databases, do you already see multiple databases setup? That would be a good indication to see if the two blogs are sharing a database or have separate ones already.
Please let us know if you have any further questions at all.
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