Does this sound like the early start of labor?

Ok so about 3 days ago i lost a big glob of mucus (presuming my plug) it had no blood in it. I have been constipated all of my pregnancy :( But a couple of days ago, i pooped really well and lot's of it! Now today i have just noticed some discolored discharge in my undies (brown). I called the doctor and she said it sounds like my bloody show. I am 37 weeks pregnant. I haven't had any contractions out of the ordinary aside from a few braxton hicks here and there. Does this mean i will go into labor soon?? Will the baby be ok if born at 37 weeks?