FTM w/ questions

Just turned 37 weeks and I'm feeling a big difference on where my baby moves I can feel my baby move on my lower stomach I've been doing a lot of walking in hopes that my labor goes great but I'm a little concerned if my baby could be coming sooner than due date? What was your experience and should I be worried if baby is getting ready to come at 37 weeks ? What are some symptoms I should b aware of...sorry I'm a FTM just looking for some answers thank u in advanced and have a wonderful day!