Hi there. To erase your browsing history from this built-in browser, tap the Menu button and select Settings. From the Settings screen, scroll down to the Privacy settings section and use the following options to clear different types of browsing data: Clear history, Clear cache, Clear all cookie data, Clear form data, and Clear location access. You can also use the Clear passwords option under Security settings to erase the passwords you’ve saved in the browser.
To erase your google search history(if you are using the Google Search Widget), From the search screen, tap the Menu button and select Settings or Search Settings. If you’re using a newer version of Android, you’ll find the menu button near the bottom of the Google Now screen. Use the Clear on-device search history or Clear on-device history option to clear the list of Google searches made from the widget.
Let me know if it works. Good luck!