May baby going to be April baby?

Ok ladies, I went to the Dr this morning and he checked me because I've been having pressure and lower back pain. I am 3cm dilated and 70% effaced already. They done an ultrasound to weigh him and his head was so far down they couldn't see it. The Dr said he could feel his head when he checked me. Ever since that I have had really bad lower back pains ( worse than before ) and it come around to my belly. It's consistant. He told me if my baby wanted to come he wouldn't stop me. I am 35 weeks. My questions are..... am I having contractions because this is my first baby and I have no idea what to expect , when will I know to head to the hospital because we like an hour away and how much longer do you ladies think this baby will stay in?? Thanks so much for all your answers!