Chances of first baby being early?

Ann • Very happily married💍Beautiful baby girl💗

I quit my job last August (I was promised 35-38 hours per week and ended up getting 6-10🙄) and started babysitting my friend’s 2 year old. We agreed it would be for a limited time until I found another job or she got into daycare. Fast forward 3 and a half weeks and I find out I’m pregnant! Hubby and I are excited, I continue looking for a job while babysitting. Seven months later, I’m still babysitting, things with the daycare haven’t planned out for them as expected, and I have been getting her 7 year old from school and watching him until my friend or her husband get home from work. We decided on my “last day” babysitting and I’ll be two days away from 38 weeks. My mom and my MIL think we’re cutting it really close and say I should stop sooner but I’ve heard that the chances of a first baby coming early are slim. My husband thinks I’ll be fine and I’m just letting my anxiety get the better of me. I’m just trying to make the decision that’s best for everyone without compromising my health or my baby’s health.