I am being threatened by an insurance company for charges my insurance policy didnt cover. What can I do?

They have the right to refuse to settle and sue you. But what they have not told you is that if you have liability insurance, as you evidently do, your insurer should still defend you in that case: pay for your attorney and if you lose, pay the judgment on your behalf. That's the good news: while the other side can look to get more in a lawsuit and can try to threaten you into agreeing to pay, you still have your insurer on your side. The bad news, of course, is that your insurer only has to pay--for a lawyer and/or for any judgment against you--to the limit or extent of your policy limit, so if you have a low policy limit and/or it's been used up or exceeded already (we can't tell from your question if it has been fully used up), then they won't be of any help, since again, they only need to help you to the limit of the policy.
If the insurer cannot help you or their help is inadequate due to your policy limits, then your only choice is either try to settle with them--either accept their offer or try to negotiate a better one you will take--or else let them sue and defend against their case. If you were at fault in sideswiping that car, starting the chair reaction (e.g. you hit them due to driving carelessly in some way: too fast, not looking when changed lanes, driving distractedly, etc.) you will be liable. And if liable, you will have to pay whatever losses or damages they can prove. So while you have the right to make them sue and prove their case, if you were at fault, assume they will likely win, and so trying to settle is better.