Is it possible for my baby to come early?

I am currently 32 weeks pregnant..Preterm labor runs in my family. I myself was born 6 weeks early and 6 lbs 5 oz, my brother was born 5 weeks early at 6 lbs 9 oz... My family and I have noticed that my tummy has dropped a lot. I feel like my tummy is laying on my pubic bone. I noticed that i am slowly losing my mucus plug piece by piece. I have been having a lot of discharge. Lately I have been having a lot of braxton hicks (which i never got before my 30th week) They are somewhat painful, and i feel it in my lower back... I also have been getting a lot of hot flashes. Is there a chance i am going to be having my son sooner than planned? My whole family believes I am. I would love some opinions from you mommies out there.