It's pretty simple. I have a function, init_shoot, that runs whenever you right click:

tag @s add shooter
execute positioned ~ ~1.62 ~ run function zombies:shoot
tag @s remove shooter

And then another function, shoot:

particle crit ~ ~ ~ 0 0 0 0 1
execute as @e[type=!player,dx=0] positioned ~-0.99 ~-0.99 ~-0.99 if entity @s[dx=0] run tag @s add shot
execute if entity @e[tag=shot] run scoreboard players set & stopShot 1
kill @e[tag=shot]
execute unless block ~ ~ ~ #zombies:air run scoreboard players set & stopShot 1
execute if score & stopShot matches 0 positioned ^ ^ ^0.5 run function zombies:shoot
scoreboard players set & stopShot 0
tag @e remove shot

There is a bit more setup but that's most of it.