By now, if you were injured you should have already been to the doctor and you reported the claim to your insurance company. If you haven't done those two things you might want to get them done ASAP.
You were at fault for the crash
If the accident was your fault, you have one choice and that is to make a claim under your own collision insurance. If you do not have collision insurance, you will have to pay for your repairs out of pocket.
You were not at fault for the crash
If you were not at fault for the crash and you have collision insurance, you have choices. You can go through your own insurance or go through the other driver's insurance. The main benefit of going through your own insurance company is time. When you make a collision claim, the issue of fault and responsibility for the accident is not present so the car can get fixed or totaled quickly.
There are a couple of detriments of going through your own insurance. First, you will have to pay your deductible when you pick up the car from the body shop. In the end, you will get your deductible back but it is an outlay of money up front. Second, if you do not have rental insurance coverage or a spare car, you will have to pay for a rental car when your car is getting fixed.
Going through the other driver's insurance takes longer. The insurance company has to open up and investigate the claim, which usually requires getting a copy of the police report and getting a statement from their insured. Once the adjuster gets this information, he will have to make a liability (responsibility) determination. In cases where the facts are clear cut, like you were stopped at a light and the other guy runs into the back of your vehicle, the insurance company should accept responsibility pretty quickly.
On the other hand, if the facts of the accident are disputed, time is not on your side. For instance, if you were involved in an intersection collision and told the police officer you had the green light, and the other driver also says that she had the green light, the investigation and liability determination could take days or weeks.
At this stage, if the other insurance company wants to take your recorded statement to determine liability, you will have to make a judgment call. You have no legal duty to give the other insurance company a statement. However, if the adjuster tells you that he will not repair your vehicle until you give him a statement about the accident, you will have to make a decision to either hire a lawyer or give a statement with some guidelines.
An example of a guideline would be that you agree to give the statement regarding the facts of the crash only and not your injuries. You can also tell the adjuster that she must provide you a copy of the written transcript of the statement.
Dealing with car issues can be difficult and you may be getting frustrated with the process. Just stick with it; there will be light at the end of the tunnel when you start feeling better.