You need to have two instances of Chrome browser opened (not two tabs, but two completely independent windows of Chrome). One with your personal account and the other with the company/school account:
- On your computer, open Chrome.
- At the top right, click Profile.
- Click Add.
- Choose a name and a photo.
- Click Add. A new window will open and ask you to turn on sync.
- (Optional) Turn sync on in Chrome with a Google Account for the new profile. Their bookmarks, history, passwords, and other settings will automatically sync.
Learn more on how to create and manage multiple user profiles in Chrome.