Unfortunately, you can't make an insurance company pay beyond the limits of your policy. However, you have the right to sue the at-fault driver for an amount greater than the value of your insurance policy. This means filing a lawsuit directly against the driver who caused the accident and not against the insurance company. In many cases, if your damages exceed the limits of the at-fault party's insurance policy, your only recourse will be to collect them directly from the defendant.
This can be difficult to do if the defendant has no cash or assets to pay you. In most cases, your personal injury lawyer will seek to obtain the best possible financial recovery for you through negotiations with the insurance company. Additionally, if you have MedPay (medical payment coverage) or PIP (personal injury protection), you can rely on that coverage to pay some of your initial medical bills or, at least, cover any deductibles or co-payments you may have, if you have other health insurance options. Then, you would file a personal injury claim with that driver's car insurance stating your damages, such as medical costs, lost wages, and property damage. Depending on the facts of your case, you may be eligible to request payment by filing an insurance claim with a third party or a personal injury lawsuit.
But one thing to keep in mind, especially if you decide to file a personal injury claim, is that insurance companies generally only pay within the limits of the policy. If you are looking for more money than what is offered by your insurance policy, there are a few options available to you. You can file a personal injury lawsuit against the at-fault driver and seek damages beyond what is offered by their policy. You can also look into filing an insurance claim with a third party or seeking compensation from other sources such as MedPay or PIP. It is important to remember that when it comes to seeking compensation beyond what is offered by an insurance policy, it can be difficult to do so without legal assistance. An experienced personal injury lawyer can help you navigate the process and ensure that you receive fair compensation for your injuries.