Can I try going into labor?

I'm 35 weeks but my baby is measuring 37 weeks. I've had A LOT of Braxton hicks this pregnancy (this is my second baby) and the other day I went into the hospital for contractions which they gave me the shot to stop them. It didn't work and they came back an hour later so I went back in. They said that I'm measuring big enough that they're not going to try and stop it anymore and told me to come back when I can't talk through them. I'm so ready to get these contractions steady so I can get this big baby out! My son was born 9.5 pounds at 38 and a half weeks.

Think I'm okay to start going into labor? Any suggestions on how to get things progressing more?

I am not a high risk pregnancy btw