Very slim at best.
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: firstname.lastname@example.org; Phone: (866) 456-8654; Fax: 212-964-0440; Cell: 212-202-0325. The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter.
Only if you can convince the US Embassy that because of your severe medical condition, you had no option except to overstay.
(213) 394-4554 x0 Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
It depends on the circumstances and the officer at the consulate. I can tell you that I recently did an F-1 CP case for someone who had to withdraw their application for admission at the POE for unauthorized employment while on her previous F-1. her visa was cancelled and she was sent back. We reapplied and I was surprised, but she was granted her F-1 and returned to the U.S. I will say this, most likely you have an alien number now so if you do any application make sure that you include that number so that the officer at the consulate post will know that you are attempting to be as open and as honest as possible.