Sorry they sent you home Bel!
Your story sounds like how my own would have played out if I had gone in yesterday...the contx were great but I didn't end up going in since they never got worse and today I was only at 2 cm at my appt. I would have gone only to be sent home (and have done that in the past!)
Anyways, it's a good sign that they are continuing- picking up even- when you try to sleep. I bet it's the real deal for you and things are going to progress for you over night....hopefully you can get some rest, if not sleep, before it's time to head back in to the hospital! I'll be thinking of you!