Welcome to the forum.
As you say, you already have access to painkillers, so a doctor isn't likely to be able to help you. I would recommend you go to see someone who specialises in treating back problems rather than a "general practitioner".
The spine is actually remarkably strong and your pain is most likely coming from the protective reflex muscle spasm that gets triggered with a nasty fall like that.
I recommend a combination of massage
and joint manipulation
to relax the muscles and realign the spine, then some postural and stabilizing exercises to maintain good biomechanics.
I hope this information has been both informative and helpful for you.
You can consult me again directly through my profile http://www.healthcaremagic.com/doctors/dr-saurabh-gupta/64132