You are currently unable to manually upload your CDC card for the Wallet QR code.
You must use outside apps that will validate/verify your status. In your case, the initial two doses may be accessible with an app for your primary healthcare provider, i.e. myHealth. Your booster should be available using the Walgreen's app.
However, it's possible you either do not have a primary care app or haven't linked your booster to a Walgreen's account. I'd suggest you go to your State's website for vaccinations to see which, if any, apps they are currently linked to.
I know this isn't the clear-cut and easy solution you're looking for, but I'd encourage you to continue working on it because it's very convenient. At worst, simply take a photo of your card and keep it stored on your iPhone.