No, your followers won't able to see what you see or search on Instagram. Moreover you can like any uploads, and search your liked page ,people and your follower's won't able to see your path. My humble suggestion to you please see the private and security policy of Instagram you get more information about their products. Enjoy :)
Data limits. Data collection limit. Every user interaction can be sent to Analytics as an individual hit, including (but not limited to) each pageview, screenview, event, and ecommerce transaction. As a result, a single session can result in many hits.
Set an expiration date for a restricted file. Authors can use the Set Permissions dialog box to set expiration dates for content. For example, Ranjit might also decide to limit both Helena's and Bobby's access to this document to May 25th, and then the permission to the document expires.