The babies usually drop 3 different times. 1st time around 2 months from due date . If you are like typical baby, just recently dropped into the beginning of birth canal. That would explain the pressure and pain you are having down below. By the time most woman go into "full" labor they are already dilated to 2 or 3 cm. So yes it is perfectly normal.
Labor is like this pain starts in stomach or back spreads out as the intensity grows then it declines in intensity. They come on a time schedule. If it b/h there is really no schedule they are minimally intense and have no order or tyming to them. If the pains keep growing in intensity and within 5 minutes apart and contimue for long while then you might be in the beginning of labor.
But obviously something is happening for you are beginning to open down below. So call them true labor or call them b/h they are beginning to do something.
Baby will drop again 2 weeks from due date, then again the day before delivery. If you loose this slimy mucus thing with little blood in it, this is completely normal. Usually happens within 2 weeks of delivery. But in my case they came out within 2 months before delivery. Dont worry that is normal
good luck sweetie