If you have a public account, you can turn off the ability for others to re-share your posts.
To stop allowing others to re-share your posts:
Instagram app for Android and iPhone
Tap
or your profile picture in the bottom right to go to your profile.
Tap
in the top right.
Below How others can interact with you, tap Sharing and remixes.
- Tap next to Allow post sharing to stories.
When this setting is turned off, users will not be able to do future reposts to their story.