Up arrow should work, you can check what the shortcut is with this command:
bindkey | grep up-line
Depending on what your up-arrow sends to the terminal you might need to adjust it, use Ctrl-vUp to check. Use:
bindkey "KEYS" up-line-or-history
bindkey "KEYS" up-line-or-search
to fix it.
Shared history is enabled with:
There may be some other options you want to set to avoid duplicates etc., see
Here's what I use:
They've been added incrementally, so some of them might be redundant.