Going into labor at 35 weeks?

I had my regular check up with my doctor yesterday at 32 weeks. She told me everything looked great with my pregnancy but i was measuring smaller than normal so she set me up for a growth scan just to get a weight on the baby. We talked about how I’ve been having Braxton Hicks contractions daily for a couple of weeks now and how I’ve been very uncomfortable! Plus I’m still working full time on my feet all day and extremely active. She said my body is preparing for labor and she thinks I will go naturally just because of how my pregnancy has progressed.

She told me that at this point if i go into labor at 35 weeks or after they will not try to stop it! Is that normal practice? I’m a little freaked out now. That’s less than 3 weeks away!! I know baby will come when he’s ready but I’ve always had a feeling he would come in March and not April 🤷🏼‍♀️

Anyone have any experiences like this?!