That will clear your Browser's search history, but not your Google Search history. Are you looking to clear that? To do so, you need to log into Google on a desktop browser. Then:
1. Click on your account picture at the upper right, select Account.
2. Scroll down and click "Manage your web history" under "Other Tools."
3. Now click on the gear icon at the upper right, and click on Settings.
4. Click on the "delete all" highlighted text.