Hello, I'm at 38 weeks pregnant. I arrived at the hospital on Saturday…

Hello, I'm at 38 weeks pregnant. I arrived at the hospital on Saturday with false contractions. My cervix is loose and mature, ready for labor. Yesterday, my plug came out. The second night of pain in my lower back, but it's all okay. It comes and goes during the day. Today, the doctor said the head is still high. Has anyone experienced this? What do they expect now? I don't know. Now that I'm home from the hospital, there's no point in going back. It's 150 km away.