You've been around a bit, and have run Amazon (now Prime Video) for some time. So, yeah, something odd must be going on.
You should know that do not need an SD card (actually, microSD card) to run any app on Roku. Now, it may have suggested you add a microSD card, but really suspect it didn't say you need one.
Remember that when there are a lot of apps on a Roku device, and when you then launch an app that takes up a lot of space, it may need to remove some less-used (or, actually, longest time since used) apps. That will cause a notice that a microSD card may be suggested. But it is not required. If you get such a message again, actually write down what it says. Take a picture, if necessary. If it's saying a microSD card (or SD card) is required, share the exact wording, and, if possible, a screen shot.
Now, if I'm reading correctly, you've removed Amazon (Prime Video) from your Roku. If that's the case, ensure it's fully removed by rebooting the Roku.
Next, on your computer, log in to Amazon. Go to the Registered Devices page (https://www.amazon.com/gp/video/settings/your-devices/
Scroll down and remove any that could refer to your Roku device(s).
Log out of Amazon on your browser. Remove all cookies and Local Storage for Amazon, or any Website that contains "amazon" in its URL.
Install the Amazon app on your Roku. Do not launch it yet.
Log in to Amazon on your browser.
Go to the Registered Devices page (https://www.amazon.com/gp/video/settings/your-devices/
Scroll down and confirm there are still no items that could refer to the Roku you attempted to install.
On your Roku, launch the Amazon app.
Select the option to register via the Website, using the Register New Device button at the top of the page.
Let us know what happens. If anything goes wrong in these steps, let us know where.