You need to discuss your potential case with a local medical malpractice attorney. Try using the Find A Lawyer tab on Avvo. You can also check with the websites of your local Bar Association and the American Association for Justice. Good luck.
You need to talk to a medical malpractice or products liability lawyer.
Your are going to have to be able to prove that more likely than not the shot caused the PCOS.
Also you do not mention WHEN you had the shot and the clock is running. In other words you have a certain amount of time within which you would have to file suit or else you can never recover so if I were you I would consult with an attorney a.s.a.p..
The answering of this question does NOT establish an attorney\client relationship. If you wish to hire me call me and we will talk about it, but as of now, I am NOT your attorney. My answers are intended for educational purposes only.