Want to re-paint an avatar with asymmetrical texture ie left side painted different design than right

I have an avatar that I would like to repaint with a different design on the right side as opposed to the left. Really all I want to do is paint a lightning bolt that goes from the right eye down the back of the head and through the back all the way to the tip of the tail. The main issue I’m having is that the texture I have for the avatar is only for one side that is just duplicated to the other side, and the texture is symmetrically applied to the whole model. Is there a way to paint my simple lightning bolt that starts on one side of the head and not duplicate it to the other? i have little experience with unity and also have just started messing with cats on blender, so that is the extent of my experience. I have repainted the texture with everything else i want since the rest can be painted symmetrically.