If you were not at fault, the other driver's insurance company will be required to pay for the damage to your car and for your medical bills, lost wages, etc. I agree with the previous comment that you should avoid giving a statement to the adjuster until after you have consulted with and perhaps retained a lawyer. Because you did not have insurance, you likely received a citation and may have to pay a fine.
Feel free to follow the link below to download a copy of a my free report pertaining to auto accidents. The book provides information on what to expect following an auto accident and tips on how to hire the right attorney for your case. Good luck.
Not having insurance when the other party is at fault has no lasting impact on your claim for damages. For some things, like damage to your car and medical bills, it is sometimes quicker and easier to go through your own insurance company. However, one way or another, the insurance for the at fault vehicle is the ultimate payer. In this case, it will pay you directly, rather than reimburse your insurance company. In addition, it is still responsible for things like compensating you for your pain and suffering, which your insurance company would not have been responsible for any way. You really do need to see an attorney, as the insurance company will go out of its way to convince you that your recovery is limited in ways that it is not. For example, here in Massachusetts, the insurance company will try to take a "PIP Offset" which it is not entitled to. That is to say, that it will try to offset the medical bills your insurance company would have paid had you have had insurance. It is always a best practice to see an attorney when you are injured in an accident, but even more so in your case.
Keep in mind that IF you were injured, you have one (1) year to resolve the case, file suit or lose your claim forever. Tennessee has the shortest statute on this in the nation.
Also, often when you don't have your own insurance, it tends to make the negotiation over the damages harder, because you have no leverage. You are essentially at their mercy.
Let me know if you need any help. I was an insurance adjuster before I was licensed as an attorney.
Please note that my answering this question, does not in any way mean I represent you for this, or any other case. You need to seek that actual face-to-face advise of any attorney in your area who can advise you further as to your rights.