If you went to the hospital and you weren't in established labour they would just send you home until you are. They wouldn't break your waters because your cramping irregularly.
If they are contractions they will get more intense in pain and closer together, once they get to 4-5 mins apart is when your hospital may let you stay. However you may want to call them as you are only 37 weeks.
I've been drinking lots of water and eating ice cubes and the pain just won't go away at all. Would I be able to go to the hospital and would they break my water or no?
Call you OB sweetie! Or L&D
Sounds like contractions.... that's how I was with my first and second didn't know what was going on its had me in in tears for 5days the pain wouldn't go away... but it could also be just cramps just drink a lot more water if the pain don't go away by tonight or tomorrow morning I will call Dr Or labor and delivery