The short answer is no. The long answer is also no.
The Department of Health investigates allegations and complaints of improper medical care that you've received in a hospital or in a physician's office.
The Department of Health is required to investigate any complaint made by the patient. However, it is not a system of justice. It is not like the court system that allows you the ability to seek compensation for your injuries. Instead, they can find deficiencies and require the hospital or doctor's office to correct their prior actions with a plan of correction for the future.
The only way you can get compensated for claims of improper medical care is to bring a lawsuit and go through the litigation process in New York.
There are also limited instances where key findings made by the department of health may be able to be used in your lawsuit.
The answer to the question is a resounding “no.”