Lactating before baby has arrived?

Stephanie • Horse Trainer/Breeder @ SMF Performance Horses. Vet Tech @ Taylor Veterinary Clinic. Farmer / operator @ Benedict Farms
Hello fellow moms...I'm 32 weeks and I have already started lactating. My breasts got really sore, hot nipples and then sure enough out comes the milk. I won't leak milk but if my breast is pressed against or I squeeze it there is a good flow. With my first child my milk didn't even show up until almost a week after he was born. Now I'm so uncomfortable...I feel like my breasts are full and that baby needs to feed. Is this normal? Does this mean I will have baby before my due date? My body seems ready now but I still have 8 poor boobs!!! OUCH!