The solution is, as you suspected, to create a second account. You’ll need a different email, so just register a gmail or something. Do NOT use an old email of yours; I guarantee somebody will figure it out if you do that.
And don’t link the two blogs, ever, not even in the blogroll.
Also, for that second blog don’t ever leave comments on other blogs when you’re signed in. Use the public blog’s username to leave comments. Otherwise even the most skillful among us will slip up and leave a comment in Persona A when signed in under Persona B.