After having been in a major car accident years ago, I know all about back pain. The first thing I would recommend is that you go get checked out (by a doctor, MRI, etc.) to make sure nothing serious happened, like a herniated disk. Alot of disk herniations happen and people don't even feel it. Then it may be years later when you have major crippling pain from it. Best to correct it when it first happens.
I would also suggest reading John Sarno's book, "Healing Back Pain".
Your next step would be to find a physical therapist. A good one will be your back's best friend! In my experience, they are more knowledgeable than doctors and what they do can really make a huge difference.
Heat is good too.
I would not recommend taking any NSAIDs (Motrin, Advil, etc.). They all significantly deplete glutathione, which is an antioxidant that your body does not manufacture, and is necessary for energy, for cell regeneration, and also for the immune system to work well.
There are plenty of natural muscle relaxers/pain relievers that I would suggest. For pain, Valerian Root. For muscle relaxer, mullein root. They come in tinctures that you should be able to get at any health food store. For pain, you can also try homeopathic Arnica Montana (great for muscle soreness too). As FYI, you can also use it to prevent muscle soreness. For muscle soreness, dosage of 30c is good. For an acute pain like you have, I would use the highest dosage, which is 200c. You should also be able to get these at the health food store. One company is Boiron, whose 30c comes in a small blue cylindrical container and 200c comes in a lavender container. Another one I used that was a big help for me after my car accident was Formula 303, which I got from my chiropractor. I think you can also buy it online. It is a natural muscle relaxer and worked much better for me personally than any of the prescription muscle relaxers or heavy duty pain medications my doctor prescribed (and with no side effects).
Movement that does not aggravate is also good. Listen to your body. If you go easy and bike and you feel like it is not aggravating, go for it. Also I would suggest looking into Yamuna body rolling (
www.yamunabodyrolling). Get a yellow ball and her book and do the back exercises. This also made a huge difference for me. The ball is also great for anyone who exercises. You are unwinding and realigning the muscles correctly when you work with the ball and do the exercises. It is great for anyone who exercises, as exercise will start to bunch muscles up and they won't work as efficiently. She explains all of this much better than I'm doing in her book. You can get her book at Barnes & Noble or on her website.
Hope this helps. Feel better!