My 4.5 hour labor

Went in today to be induced at 39+3 and 4cm dilated. They started pitocin right around 10 and broke my water at around 1030. Contractions started light like what is been having before then within 30-45 it got BAD. I only had back contractions, nothing in the front. It felt like my tail bone was breaking, that’s how bad it hurt. So I got my epidural at 12 (that was test dose) and I was 6 cm dilated. then according to the chart, my contractions were strong but I felt no pain only pressure. I was shaking bc I was nervous that that pressure in my butthole I felt was her trying to come NOW but I wouldn’t know bc of the epidural. They were like no you’re fine. I did not feel so. Like it felt like I have a huge poop to push out. So 1:30 she came to check my cervix and she was like ...I think you can push. I pushed about 45 min before the dr got there and legit 5 min after he got here she came out. The part that was the worst was after her head came out when I had to push her body bc I had no rest. She was born at 2:31 at 6lb 8oz, 19in long.