Your IP address is most likely the giveaway when you attempt to access region-locked apps on a Firestick from abroad. Fortunately, you can change your IP address by connecting to a Firestick-compatible VPN such as ExpressVPN.
You might need to change the location in which the Firestick is registered. You can do this by going to Amazon on your desktop or mobile device and going to Accounts & Lists > Your content and devices > Preferences > Country/Region Settings > Change. From there fill in the form to change your country on Amazon.