Feeling discouraged

Im 36weeks and 4days. The past two nights ive had contractions that are able to be timed and almost hit the “real labor” mark before they slow down. My back is killing me, im having contractions in my back as well, powerful period like cramps, and nausea. Ive also definitely been losing my mucus plug. I had my 37week appointment today: early bc 37 falls on thanksgiving, i was supposed to have my cervix checked. When I mentioned to the doctor I saw today (not my regular doctor) she basically told me the “thats pregnancy for ya” line and they cant check my cervix because im not 37weeks yet, and if i were to go into labor they would do everything to stop it bc im not 37weeks yet. This is entirely wrong right? I know plenty of people who have had their babies at 36weeks and they let them have the baby normally. And with all of this info, they should have checked me right?

This is my second baby- the first my water broke naturally and I didn’t have contractions until much later. Im sort of clueless but not that clueless.