It sounds like you are in early labour though. As soon as your contractions get 5-10 minutes apart make sure you call your doctor as they will probably tell you to come in.
Unfortunately your water probably will not break on its own. So do not wait just for that before you go to the hospital. It could break, but it doesn't for the majority of woman. I didn't know that until recently. My water broke with my first at 36 weeks. It's definitely not like the movies either if it does break on its own. Mine came in a big gush while I was sleeping (woke me up) and continued for the hour drive to the hospital and through out my 16 hours of labour. I was surprised at how much liquid was actually inside me.