Due date changes

I went to he dr today and got an ultrasound done. Based on my last period I would be due June 10th. However based on the ultrasound I’m due July 6th. I recently changed my dr due to non communication issues. My baby girl is at 6lbs and 1 oz and has a strong heartbeat as well as growing. She is in the head down position and my next appointment I’ll be doing a dilation check. I’m nervous as all hell since I’ve started having contractions a little over a week ago. And the L&D; nurses last said i was 2cm dilated. My dr said if she doesn’t come on her own by week 38 he is going to induce me on week 39. Just so all the pain I feel now when I walk can be put at rest but he wants her to bake as close to due date as possible. So close and so excited.