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, then tap
Settings and privacy.
Below How others can interact with you, tap Guides and sharing.
- 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.