Here is an article from Macworld discussing several ways to store a copy of your COVID vaccination card with you in your iPhone, iPad or Mac. I took a photo of my two cards with my iPhone. The image is automatically stored in the Photos app. Then, on a Mac, Photos can be opened, the image found, then a name placed on it. "Vaccine" is what I used. Then, if you need to quickly show the photo to someone, a search on "vaccine" will quickly find the photo.

The article also discusses other ways.

Jim Hamm