Instagram has finally updated its app to add support for feature that Apple introduced to iOS back in 2014.
You can now finally share images to the Instagram app from within Photos or other apps on iOS, using the iOS share sheet extension. You will have to enable the Instagram app from the share sheet menu first and then you will see the app in the Share option.
Right now, sharing an image from other apps to Instagram does let you add caption and post the image, but you can't edit it in anyway.
The funny thing is, Apple showed this feature working within Instagram app in their iOS 8 keynote back in 2014, and it took Instagram almost two years to actually add the feature to its app. And even then the implementation isn't perfect.
You will have to update your app to the latest version to get this feature.