Instagram allows you to take photos and videos from your device photos, but it also allows you to take photos and videos for "Stories" from right within the app. Depending on how you've used Instagram, you might have copies of that content in your device already, as well as in cloud storage. For example, an Instagram user who uses their iPhone camera app to take photos (and their iPhone is configured to save photos to iCloud), then selects from those photos to create Instagram posts, is already going to have copies of those photos. However, users who take photos/videos directly within Instagram might not have any external copies.
If you need copies of your content posted on Instagram, there are several approaches with different tradeoffs.
Ok, this is not a very satisifying solution, but it gets worse - there's not just one way to get content from Instagram item by item, but several ways depending on whether you're trying to get a copy of a post or a reel, if it's public or private, and if you're looking on a browser or in the app. I'm not even sure it's possible with private reels, without going into Web page source code and scouring for content links. More information would be appreciated if folks know!
The "tom's guide" site wrote a good article on how to save these photos from Instagram.
One good option to save photos going forward is to set up Instagram settings as explained in that article, so that new photos are always saved to your device's
camera roll. Unfortunately, if there are already many photos that need to be downloaded, downloading them one-by-one is not reliable or efficient.
Some other sites advocate using browser extensions or 3rd-party tools.
Ultimately it might be easier to take a roundabout approach. Meta supports sending your Facebook and Instagram content to other online services via data portability tools (using the Data Transfer Project, supported by the Data Transfer Initiative). After getting Meta to transfer your photos to a cloud photo or backup service, that service may have better functionality for getting your own copies of bulk content - or it might solve your use case sufficiently to have that content securely backed up in another cloud location.
The source code (markdown) for this article can be found on GitHub.