6cm 80% effaced

I went to my weekly appointment this morning. I’m 38/3. Baby number 5, “a good 6cm 80% effaced soft and stretchy”

Having sporadic contractions just not super close together. They sent me home because they said I’m not 39weeks and they can’t induce. I live 30 min from hospital. I’m worried. I went from 6-10cm last baby in 45min. I don’t want to miss the opportunity to have an epidural plus I don’t want to have this baby on the highway. My question is if I continue to have contractions/go for a walk and go into hospital I should be 6-7cm easily, will they send me home???