I've been in a car accident where the other driver rear-ended me can I file a lawsuit for back injury?

You can definitely file a lawsuit, although you may be getting ahead of yourself.  The first thing you should do is file a claim with the wrongdoer's insurance company.    Very often these cases will settle so there is no need to file a lawsuit.     However, the most important thing is that you get the medical treatment that you need.  You should not discuss a settlement with the insurance company until your medical treatment is finished, and you know the extent of your medical expenses and lost wages.  You are also entitled to a fair amount for pain and suffering.  I would strongly suggest you contact an expereinced personal injury lawyer.  The first consultation is always free, so it will not cost you anything to make this call.