Can I file a lawsuit if my doctor never warned me with all the side effects of tubal ligation?

Malpractice is care and treatment that falls below the standard of care and causes injury. The failure to inform a patient of recognized and serious consequences of a medical procedure can certainly be the basis of a claim. Has any doctor told you that your current condition was caused by the procedure? It has not been very long since your procedure and perhaps it will resolve. Your first task is for someone to "name" what is wrong with you and to see if it can be treated and resolved.

Unless there was a serious permanent injury, the costs could far exceed a recovery assuming malpractice

The failure of your doctor to warn you of the risks of a procedure can be a basis for a claim. To succeed on a claim of the doctor's failure to obtain your informed consent to the risk of a procedure, you must also prove that had he fully informed you of the risks, you would have chosen not to undergo the procedure. As a more practical matter, in New York State, bringing a medical malpractice claim requires very significant investments of time and money on the part of the handling attorney. For this reason, most medical malpractice attorneys will not accept cases without very significant or catastrophic injuries. If your symptoms resolve, your injury would probably not justify the expense of litigation.