Howdy New user 2016,
Welcome and thanks for using Apple Support Communities. It sounds like you want to remove Spotlight Search history on your iPhone. I can understand wanting to keep your activity private and can help you find a solution. To do this you'll want to go to “Settings > General > Spotlight Search. From there simply toggle the switch next to “Siri Suggestions” to “Off”. This will clear any history and prevent Spotlight Search from remembering anything in the future.
Here's a resource that can help manage your search settings:
Use Search on your iPhone, iPad, or iPod touch
Specifically, use these steps:
Change search settings
Go to Settings > General > Spotlight Search.
From here, you can turn Siri Suggestions on or off and choose which apps to include in your searches. For example, if you don’t want to see search results from your Messages app, you can deselect Messages.
Take care!