There are several things you can do to protect your privacy.
(1) Clear all cookies every time you close your browser. (You should be able to make this automatic, using your browser settings.) Those alerts you got may have been made possible by cookies.
(2) Access SaSu using a good VPN (such as proton), or Tor. (Tor can be slow, so for most people a good VPN is more practical.)
(3) If you want to remove all traces of your browsing history, run software that will securely wipe files. (East Tec Eraser is good. Run it regularly, e.g. weekly.) Just deleting your browser history isn't enough, though it will defeat any casual snooper who may have access to your machine.
(4) If you are really paranoid, boot to a live OS that prioritises privacy, such as Tails, and only access the interent using Tor after switching off javascript. (You probably don't need to be that paranoid.)