Do I leave my lip jewelry in while soaking it?

I got a lip piercing last monday and I want to soak it with sea-salt, I was wondering if I can take the stud out? I want a little relief on the area because there's an indent from the stud being pulled from the outside of my mouth....from sleeping I guess? but yeah I want a little relief to be able to rub it or something because it's sore. I was thinking maybe I could do that while it's being soaked in warm salt water? Also should I use warm or cool water to soak my piercing in? if someone could help I'd appreciate it a lot. Thanks!