Am I in early labour?

I’m 41+3, booked in for induction at 9:30am had the propess at 12:30pm baby was monitored for 30 mins after. Then I went for a walk around the hospital for 30 mins with my partner. Came back to the ward, started getting a few little niggly pains and a little bit of backache (midwife said good sign) got sent home as outpatient because I’ve had a straightforward pregnancy and me and baby are all healthy. Was told that the propess takes 24hours to work and if no sign of labour, to come back In tomorrow at 12:30pm for another propess. Started getting more backache and period like cramps around 2:30pm then it really hit hard and went all into my back around 4:00pm really strong pains all in my back, tummy went extremely hard, hips and legs started aching, tummy started cramping, bounced on birthing ball breathed them through, managed to get to sleep for an hour around 5pm. Woke up at 6pm back is still in a lot pain, tummy is still ROCK hard, not really felt baby move and still got cramping but no worse than earlier the pains are still the same, peeing quite frequently and a strong urge to poop like I have a bad tummy, also very sore vagina like it feels very swollen..

Does it sound like a success with the propess and I’m officially in labour?