Definately go to your doctor right away! Get any tests your doctor prescribes because your back and ribs are a big deal! You don't want to have back problems in the future!
Until you go to your doctor, don't do any strenuous exercize or anything that hurts. Use ice to reduce inflamation. Take appropriate over-the-counter pain medication if you need it.
Depending on your auto insurance, your medical expenses will probably be covered 100% by the auto insurance company. Bill the auto insurance, and not your medical insurance. This can save you TONS of money if it turns out to take a while to heal, and especially if something happens to your medical coverage.
If there was someone else at fault besides you, then you may want to look at your legal options. Just incase you do go the legal route for compensation, it's very important to keep records of everything relating to your injury.
To help both your doctor and your insurance/legal claims, answer these questions every day or two:
What hurts? (Injuries may cause referred pain or pain due to compensation or overuse.)
How bad does each injured part feel on a scale from 1 to 10?
What type of pain is it: piercing, throbbing, burning, etc?
What helps the pain?
What makes the pain worse?
Have you missed work?
Have any basic tasks become dififcult?
Since the injury, have you received help around your house?
Good luck, and feel better!