As u described above, I can surely say that, there injury at sacral region as well as in lumbar disc due to force of fall. And the pain while coughing is due to increased pressure in disc area while cough.
Next Steps
you need rest to allow your injury site to heal. use ice pack 2,3 time daily, along with your medication. rest is must
Health Tips
avoid prolong sitting and traveling which gives you jerk in spine, it will increase pain and delay recovery.. so avoid that..for 3 week.
please consult online for physiotherapy for in detail guidelines for complete recovery