A fall on the coccyx bone (tail bone) can REALLY hurt. The pain can last a long time.
I fell off of a horse back landing straight on my coccyx bone, back in 1992. The impact was so hard that I got a concussion (falling on your tailbone, not just hitting your head) can jostle the brain and cause a concussion. I did not break or fracture anything BUT the pain lasted for 3-4 months.
Definitely get it checked out. Ibuprofen is good as it's an anti-inflammatory...so it will help with muscular inflammation. A muscle relaxer like Flexeril or Skelaxin might be in order, too....but you need prescriptions for those...so see your doctor.