Auto Insurance Claims: 4 car accident, insurance, rear end collision

Question
Can I file a claim on all 3 insurances? I was driver 1 and driver 2 was traveling behind me, and driver 3 was behind driver 2, and driver 4 was behind driver 3. Vehicle 1,2, and 3 slowed for traffic while driver 4 failed to reduce speed and made contact with the rear of driver 3 pushing it into the rear of driver 2 causing driver 2 to make contact with the rear of driver 1. Driver 4's insurance is paying for my car to get repaired but I am suffering from a cervical sprain to my neck and lower back injuries.

Answer
Without knowing more about the specific sequence of events and how fast/closely cars 2 and 3 were traveling, it is impossible to say for sure.  However, it is certainly possible that you could prove negligence on the part of all three drivers and obtain recovery from each of them.  

However, in reality, it is likely that if you submitted a claim to the insurer for cars 2 and 3, your claim would be rejected on the basis that driver 4 was the only negligent party.  In order to recover from them, you would likely have to file suit and to find out more about each of their version of the events.  Also, the laws of apportionment of damages could make it irrelevant whether your claim is against car 4 alone or all four cars, though you would certainly need to consult with a competent lawyer in your jurisdiction to determine this.  

Please keep in mind that my experience is in Georgia, and under Georgia law you would certainly have a potential claim against all of them.  This is also the general "common law" of torts.  However, it is possible that your jurisdiction could have specific rules about how to deal with this situation.

Since tort law is different in every state, and I only practice in Georgia, it is difficult to answer your question definitively.  But to conclude, yes, you should be able to make a claim, but depending on the stories of the other drivers the claims of one or more may be rejected.  I, however, have certainly recovered from multiple drivers in scenarios just like you describe.  

Hope this helps!