That's all you're going to get from the insurance company. Even if you take the insurance company to court, you will not get a judgment for more than their policy limits against the insurance company.
If you take the driver of the other vehicle to court, and prevail, you could get more. There are a lot of factors there. Talk to a lawyer. Most will take a contingent fee.
I have a suggestion. Go to a lawyer, and tell him that the insurance company has offered $10,000.00. You already have that offer. Tell the lawyer that you will agree to give him 1/3 of the settlement/proceeds that exceed $10,000.00. After all, why should he get 1/3 of the $10,000.00. You already have the $10,000.00 if you want it. He hasn't done anything to deserve a fee on that amount.
I've heard of people doing this, and it makes sense to me. Some lawyers might not agree to that, but, at least ask and shop around. There's plenty of lawyers out there, especially in the personal injury business.
Find a lawyer that will agree to put that in writing in the fee agreement.
Good luck!!!