Can you actually get sick from getting your wisdom teeth pulled out?

No. nobody die after getting wisdom or any other tooth removed . your dentist will recommend you few medical tests prior to tooth removal appointment in case if you have any systemic (whole body) problems or you show any of the systemic symptoms . dont hide any of your medical/dental history or any medical condition . otherwise it may led to complications. and dont be afraid of the procedure , talk to your dentist in case of anxiety .