thanks for your question.
from your description, your problem looks like coccydynia
, which is pain and inflammation of coccyx(tailbone).
As far as the treatment is concerned, start using donut cushions while sitting (even when you are travelling). and hot fomentation- by sitting in a shallow tub filled with warm water (twice a day for 15 mins each)
you can take the help of a physiotherapist for further treatment and exercises. And in your present situation only exercise will not give complete relief.
If still the problem persists, you can go for X-ray, and then treatment with medication accordingly.
I hope this will help you
wish you good health