The Insurance co will pay the policy limit. You can sue the driver for the rest, obtain a judgment and enforce in order to collect all your damages.
Word of advise here, the Insurance co will ask you to sign a release of all claims, meaning that once you receive the check you can not sue the driver, it is standard practice for them.
Do not sign a release unless paid in full, you're not obligated to sign it in order to collect all your damages, either.
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