Your health comes first. And running secret gift exchanges does take a lot. It's a really cute idea, and even if you can't do it this year, there's always the chance in the future you can do it again.
I'm not sure if you'd be able to find any help in other secret exchange groups, but there are a few that are active. I can't remember which one, but I know there's one I recently joined that offers a summer Santa event. You could see if any of them would be willing to help?
I've never seen an Easter one, so it was very charming to run across! Even if you are unable to revive it, the idea alone is enough to make some people smile.