Color Correction – How to prevent my camera from exaggerating skin color differences?

The skin color of my subject is very disparate and I am not sure of the reason. For me, it seems that the side of the face suffers from a shadow of color projected by shiny hair. At the same time, the color of the skin that is close to the center of the face appears as an exaggeration of slight differences in the color of the subject's skin. These red / pink spots are not really visible to me.

What is the best approach to avoid such problems, because I take a picture so I do not have to try to repair it in Photoshop? Is it something with my settings? Woman's face crop with exaggerated skin color differences