A simple solution to this is to use Profiles in Google's Chrome browser. Basically, it's like having 2 different browsers - one for your personal account and one for your work account. This will help ensure that you keep those 2 worlds separate!
Instructions for setup can be found here: https://support.google.com/chrome/answer/2364824?hl=en
When you setup the accounts, assign different icons and themes to each account so you can easily see which window is logged into which account.