Don't change your password unless your current password is compromised. If you're still the only one who knows it, WRITE IT DOWN ON PAPER, and keep that paper with your important stuff.
Then, go to your Wallet, and click Permissions. Copy and paste those "keys" into a text file and save it somewhere, apart from your main password which is on paper.
Then you can log out of that browser without worrying you'll never get back into Steemit. But of course, don't do that until you're sure you've got your correct current password safely written on paper.
Sorry to be redundant with the instructions but it's quite important.
Also, I'm not the expert in this stuff, I'm just trying to help you because you asked. I'm pretty sure it's correct but don't quote me.
RE: Penny Freeman, former staffer in tears over Ron Paul betrayals