Hit shin on rim of tub, not bruised, swollen, warm to touch, discomfort but no pain, swelling does not feel like fluid inside, no discoloration. Help?

How long ago? Swelling is normal after a traumatic event. Rest your leg and apply ice to the area. See a doctor for persistent pain or inability to walk.
Bruise. Shin bone (the Tibia) injuries can be painful. There is not much fat or muscle that protects the bone in that area, so it can be painful when you Bruise your bone there. If it gets red, starts to hurt and or swell, and gets hot, there is the cause for cellulitis and you would need to see the Dr. Otherwise, resting the area, and trying an Over the counter nsaid like aleve (naproxen) or Ibuprofen may help.
Not much we can do. About that online. It's certainly not a typical sounding injury, but I don't know how long ago this happened and what other things might be contributing. Sounds like the leg needs to be looked at. Urgent care is your best bet since they have x-rays on site. Good luck and feel better!