Unless you smell pee, it ain't pee! Check in with your Dr asap!
Yeah i don't think its pee. It sounds like your water broke.
Not all contractions get stronger once your water breaks. My friend had her water break and not get contractions until 2 days later. She was on constant observation from her midwife and everything was fine. But if you tested positive for group B strep, you need to go in right away so they can get IV antibiotics into you.
Im surprised your doctor hasnt already talked with you about reasons to go to hospital or call after hours. It does sound like your water broke. Without contractions, that is called early rupture of membranes. That is reason enough to go get checked out. Since your risk of infection and potential risk to baby increases after water breaks, doctors usually want you to note the time and head to the hospital so they can get baby out within 24 hours.
Sound like your water broke to me.
If it happens when you lay down, odds are you are leaking amniotic fluid. Probably not peeing. The baby's head will block your cervix when you stand up, usually. And then once you lay down and baby moves, another gush. Call your doctor this morning, even without contractions. They will check and tell you what's going on. Good luck.