For your safety know that you can quickly delete your search history . This can be done easily by pressing CTRL then H select "clear search history".
Delete Internet Browsing History for Mozilla Firefox
Step 1.Click the menu button (show to the left) , choose History, and then Clear Recent History….
Step 2.Select how much history you want to clear: Click the drop-down menu next to Time range to clear to choose how much of your history Firefox will clear.
Step 3. Finally, click the Clear Now button. The window will close and the items you've selected will be cleared.
Visit Mozilla Firefox support page for more details