I have a sharp pain in left ovary with pain radiating around to my back and down my leg. would that be a cyst?

You, could be: an ovarian cyst commonly causes a dull ache that may radiate to your lower back and thighs; pelvic pain shortly before your period begins or just before it ends, and pain during sexual intercourse (dyspareunia). Ovarian cysts usually resolve without treatment. It is important to consider other things that might be causing your symptoms that may need to be treated, eg. urinary tract infection.