I am a 40 year old female had my upper left wisdom tooth removed 4 weeks ago and a few days ago I started feeling pain in that area after inspecting I saw another full molar growing at that spot its half way cut through the gums is this normal.

Wisdom Tooth. I suggest you see the surgeon who extracted the tooth. They have radiographs of the area and know exactly which teeth are present and which teeth are missing. You may be mistaken about which tooth was extracted.