Regarding homing projectiles.

I would like to make an item/tome that upon left and right click makes 3 projectiles that home towards the nearest player/mob giving the regen effect upon hit on left click and deal knockback and low damage on right click. Was wondering if this was possible using carrot on a stick and the projectiles shulkers fire ( preferably not the shulkers shells because i want smooth travelling. ) and how id go about making it.