When to go to L&D

So! I’m 37wk3d and I am being induced Saturday.. however .. I’ve always had contractions since 32 weeks. Nothing serious just irregular and somewhat uncomfortable. Well started yesterday they became more painful, sometimes stronger. Today, definitely back pain is there and back labor I feel. Along with the cramping and pain in the front. I got checked yesterday at my MFM appt and I was 1cm and 25% effaced. I’ve also been loosing mucus plug the last three days. How long would you guys wait before going to L&D? They will not admit me until I’m 5 cm or in tons of pain. Not sure what their level of pain thresh hold is before they say oh ok, we’ll keep you now .