Labor?

With my first my water broke on its own so I never had to time contractions or anything. With this one I've been having moderate to painful contractions close to 4 minutes apart for a few hours but I fell asleep for 4 of those hours so I'm not sure if I should go in or not. Do I consider them painful if I can still sleep through them? My hospital is very strict about who they'll admit. They won't take you unless your over 3 cm and have been having contractions for over two hours less than 5 minutes apart. And even then it's iffy.. I'm 37 weeks and have not been checked for dilation yet.