Thanks. I don't know the specifics as I'm not tech minded but I always think that might be the case. Never actually look at anything when I'm at work. Unless it's my phone on 4G but understood
All networks log the addresses of where their users go on the Internet, your broadband ISP does, your mobile provider does, any network you have a username for does. You can't erase that log (unless you have admin rights to that network) because it happens outside your computer.
Never operate a PC, especially a shared one, without setting up password protected user accounts on it to ring-fence each user's activity.
Safer practice on a personal PC that's rarely shared, especially if you're going to be prowling porn and other personal content that could be embarrassing or exploited, is to create a separate account that doesn't have admin rights on that PC and use that to do your dodgy browsing.
If your searches are "precious" then save the results! You have a host of apps on your PC that can be used as notepads and there are countless options for free or paid account-based note-keeping on the Internet (almost all of whom are "reading" what you're saving in order to sell your "anonymised" habits to advertisers).