Maybe this will make things clearer for you regarding Nestorian heresy and the title Mother of God.
“It concerned the nature of Jesus Christ, the Second Person of the Holy Trinity. Nestorius taught that the Virgin Mary gave birth to a man, Jesus Christ, not God, the “Logos” (”The Word”, Son of God). The Logos only dwelled in Christ, as in a Temple (Christ, therefore, was only Theophoros: The “Bearer of God”. Consequently, Virgin Mary should be called “Christotokos,” Mother of Christ and not “Theotokos, “Mother of God.” Hence, the name, “Christological controversies”.
Nestorianism over emphasized the human nature of Christ at the expense of the divine. The Council denounced Nestorius’ teaching as erroneous. Our Lord Jesus Christ is one person, not two separate “people”: the Man, Jesus Christ and the Son of God, Logos. The Council decreed that Lord Jesus Christ, the Son of God (Logos), is complete God and complete man, with a rational soul and body. The Virgin Mary is “Theotokos” because she gave birth not to man but to God who became man. The union of the two natures of Christ took place in such a fashion that one did not disturb the other.”