Like Twitter, Instagram profiles were made to be shared with strangers.
Unfortunately, anything strangers can see is also visible to someone looking to scam you.
Instagram allows your account to be made private. This means your posts will only be available to your followers.
You can find out more about private accounts here.
This article shows you how to make your account private.
While this is a dramatic step, it may be worth it to stop scammers harvesting your information.