Hi,
I closed my pinky finger in a door 5 days ago and a doctor put a splint on me and I was diagnosed with a sprained finger. Ive noticed my skin is extremely soft, imagine an eldery person soaking in a bath for hours. And just today I noticed bleeding under my skin and the finger turning brown. Im scared this will be permanent and my sprained finger is something more!! What can I do?

The brown is blood, a bruise that moved from a deeper area to the surface. Like any bruise, eventually your white blood cells take it away.
You could have broken a bone. Without an X ray you don't know, but the treatment is the same - a splint.
I have one, possibly two broken fingers. One is old and has thickened a lot and I can't even bend it any more. You may get the same, or at least knobby arthritis. Or it may heal completely and not hurt again. This is just the way it is with fingers.