In French, there are two very close expressions to express the nuance between hurting someone physically and hurting them emotionally.
Look at these sentences:
To express to hurt someone (physically) in French, you use the expression faire mal à + person. (literally to do hurt to)
To express to hurt someone (emotionally), you use the expression faire du mal à + person. (literally to do (some) hurt/damage to)
To use both these expressions with to hurt me/you/him/her/us/you/them, you will use me/te/lui/nous/vous/leur before the whole expression in simple and compound tenses, and between aller and faire (du) mal in Le Futur Proche.