I don’t know about being friends. I’m really struggling with this myself. On one hand, the man/woman didn’t do anything wrong if they decide not to continue the relationship (if it’s done respectfully) so a friendship may be a nice thing that comes out it. On the other hand they rejected me purely because of HSV and it’s going to hurt to watch that person date someone else. I’m leaning towards not being friends as it’s just a painful reminder of rejection.
Regarding shame, it’s hard, but try to get over it. It’s nothing to be shameful about. Think about it, millions of people did the same thing you did, you just were unlucky. There’s a lot of things worse in life to be worried about.