Can I sue for medical negligence due to the premature birth of my son if I was sent home when in fact I was in labor?

You should definitely speak with a medical malpractice attorney, since if malpractice were involved, you deserve just and fair compensation for your loss. Whether or not this was malpractice will depend on whether sending you home was what the "average reasonable doctor" would have done, based on your condition and the observable and reported symptoms. Medical malpractice is, to oversimplify, basically medical negligence; a doctor or hospital or other care provider is potentially liable to the extent he, she, or it was unreasonable careless or did not provide care that lived up to prevailing accepted medical standards. To determine this more fully generally requires expert help--e.g some doctor evaluating the situation and care. However, experienced malpractice counsel would be in a good position to do a preliminary evaluation and decide whether there may be a case worth pursuing. Good luck.