To help you out, chiropractors and their practice are full quackery and pseudo-science. HOWEVER, osteopathic medicine practiced by a DO is real medicine. Osteopathic medicine and osteopathy are two related but different things. The difference being that osteopathic medicine originates from osteopathy but they ditched all the pseudo-science and actually backed it up with science.

TLDR: If you want to get your back cracked scienctifically, find a Doctor of Osteopathic Medicine (aka a DO).