Searching through history with up and down arrow in zsh

You had up-line-or-search bound to your up-arrow. This should do what you want:

bindkey '^[[A' up-line-or-search
bindkey '^[[B' down-line-or-search

[Edit]:

The command above only uses the first word to search. The following will use the whole line. See man zshcontrib...

autoload -U up-line-or-beginning-search
autoload -U down-line-or-beginning-search
zle -N up-line-or-beginning-search
zle -N down-line-or-beginning-search
bindkey "^[[A" up-line-or-beginning-search # Up
bindkey "^[[B" down-line-or-beginning-search # Down

I'd highly recommend using "$terminfo[kcuu1]" or "$key[Up]" rather than hard-coded stuff like "^[[A" which may or may not work on any particular system.

Check out /etc/zsh/zshrc for more keys. Here's what it looks like on my system. I think the terminfo keys are more likely to be defined.

key=( BackSpace "${terminfo[kbs]}" Home "${terminfo[khome]}" End "${terminfo[kend]}" Insert "${terminfo[kich1]}" Delete "${terminfo[kdch1]}" Up "${terminfo[kcuu1]}" Down "${terminfo[kcud1]}" Left "${terminfo[kcub1]}" Right "${terminfo[kcuf1]}" PageUp "${terminfo[kpp]}" PageDown "${terminfo[knp]}" )

https://unix.stackexchange.com/a/405358/276872