End of pregnancy and no early labor signs

I am 37 weeks pregnant and I really haven't had any signs of labor besides the lightest braxton hicks contraction here and there. There's been no swelling, I'm not achy or overly tired. Still active and feeling well. Does this mean I may be a long way from labor? I'm almost starting to worry that my due date may be way off even though they did a dating scan. Anyone else experience something similar?