Does the pain come and go? If it comes and goes, time it. If the time between each pain gets short and the pain gets more intense, it would be good to go in. That is a sign of early labor as well as a "bloody show". If not, it may just be your body stretching and getting ready for the baby. It could also be Braxton hicks contractions. If you feel something just isn't right go in. Trust how you feel. I have back pain and lower stomach pain all the time plus Braxton Hicks contractions. It is horrible but they aren't frequent enough or intense enough for me to go in. I am also 37 weeks but I have been feeling this way for at least a month.
Pressure can be part of labor, same with back pain. I would definitely try calling my OB -they should have a 24 hr emergency number and advise you to either go to the er or they'll see you tomorrow to check you.