Contractions 2-5 minutes apart.

Hey ladies so I’m due 12/16 and on Sunday at 5 I started having Contractions but the timing was all over the place they started to get worse at about 9 o’clock. I came in to labor and delivery at 10:30 when they were three minutes apart. It’s now 3:45 am on Monday and they are still 3 minutes apart. I was only 1cm dilated when I got here at 10:30 pm I was being checked every hour and was progressing at 1am I was at 3cm and at 2 I hadn’t made any progress so I was told to walk to halls until 2:30am which made my Contractions worse. At 3am I was checked again but still 3cm dilated. So the on call Dr said because I’m only 37 weeks and 5 days that he can’t break my water or give me Pitocin to help me progress that I would have to progress on my own and be at least 4cm with these contractions to be admitted. So he suggested I get a pain med shot for my contractions and to go home and rest and if my water breaks or anything gets worse to come back today. I told him that I see my dr tomorrow at 9am and he said I won’t make it till tomorrow so I’m irritated like why send me home then and he said I live close enough to come back after laboring at home and relaxing at home. So I’m going home and going to sleep but when I wake up I’m going to walk etc to progress labor so pray for us! Ps: this is my 4th baby but 5th pregnancy.