On Thursday, Instagram enacted a new function when it comes to using your Instagram Stories. 

According to CNET,  if a friend tags you in their story, you will now be able to share that story, add it as a sticker, or add creativity with other graphics. It will also then link back to the original account that you shared it from.

The important part of this: You must be tagged in the post for this to happen.

So, in that case, you don’t have to worry about your personal stories being shared – but if you have a public account versus a private account, the stories are still able to been seen by whoever follows the public account.