Fell after thread on steps broke and hurt butt!

I was going down my old basement steps and the tread broke and I fell hard on my butt, my tailbone butt area and half of right butt check is so sore, I can't cough, sneeze, blow my nose or sit without being in horrible pain. I know they can't do anything for a broken tailbone, so Im not going to the doctor. How long does tailbone injury last? Ice or warmth for it?