Hello, and welcome to Just Answer. It certainly sounds like you have your hands full. From what you have described, it does sound like you would be fine to wait until morning when you are scheduled to see the vet.
If she is actually starting labor, I would be hesitant to start medicating her at this point. A little Banamine or aspirin should not cause any problems with labor, but will give her a bit of relief with any pain in the leg.
If it is warm, there is some form of inflammation or infection present. If there are no wounds visible, it is likely inflammation due to blunt trauma, thus, a soft tissue injury. Time and anti inflammatories will help with this.