Due date was 9/7 and still no baby!

I went to hospital Thursday night with contractions and chest pain and after monitoring me and doing ekg, they sent me home! I went back the next day because my husband and I were trying to speed things up and had sex and after we were done I noticed a swollen bulge in the opening of my vagina- we freaked out thinking it was my cervix or something wrong (after an embarrassing trip back we learned it was just tissue swelling from arousal and friction lol) and I was still only 3cm dilated and 50% effaced... I'm 40w 3d now and haven't had consistent contractions that are intense enough yet... starting to feel discouraged and anxious about when my baby girl will come :( I keep losing parts of mucus plug but my water hasn't broken yet. Anyone else going through the same thing or have any advice for a first time mom? I've been walking and squatting and friends and family have told me about castor oil to help induce labor but I don't want to take that route as I've read horror stories about it. I'm trying to be patient but I just can't wait to meet baby "A"!!!

At hospital, my contractions were already 2 min apart but I can only feel them every 10 min or so... the contractions are happening but my cervix is just dilating very slow.. my doctor said she would induce me at 41w and a few days but i don't know if I can wait that long!!!

I'd love to hear some labor and birth stories for encouragement!!