If you think someone could be checking what website you have visited, go to this link and click on the search engine which is applicable to you.
It shares instructions with you how you can look at websites privately and uses screenshots to show you how do this.
It’s also important to delete your history of searches too.
If you are worried someone else may have access to your private computer, then it may be better for you to use another computer at a friend’s, your work or one in a public area such as your local library.
PS: private browsing or incognito mode only prevents the browser from storing browsing information locally.
It won’t keep you anonymous online or prevent anyone else like your employer or internet service provider from seeing your traffic.