I had a long labor (48 hrs from water breaking to delivery) with my daughter. She was in the occiput posterior position and it took a while for her/me to turn her so that she could make her way out. When she had turned, she came FAST. I pushed three or four times and had a baby in my arms.
Anyway, in the process of coming out of my pelvis and vaginal canal, my tail bone was either sprained or broken. Ouch. Sitting was so, so painful - so breastfeeding was painful, eating was painful, taking a bath was painful getting out of bed hurt...most everything was very, very painful and it lasted around six months (before I felt completely healed).
My understanding (what I was told by my midwife) is that tail bone injuries are a lot like toe injuries: time is the only true cure.
That said, I found heat therapy to be a comfort and I used pillows and a donut to hold my body in less painful positions. I also used Arnica gel externally (which is very safe). I am not sure that it would be safe w/ breastfeeding, but recently, after breaking my leg, I took Bone Up, a Calcium supplement. I was able to heal from a complete (but clean) break in my Tibia in four and a half weeks.
Good luck and congratulations on your baby!