We have a policy limit of $100,000. Does this mean that any medical bills, damages, legal fees, etc. that exceed that limit are my responsibility?

Your insurance company is only obligated to pay up to the policy limits in settlement or after a court judgment. However, if you actually go to trial and obtain a jury verdict over the policy limit, the defendant will personally be on the hook for the overage. Or, in rare circumstances, if your attorney makes a "policy limit demand" and the insurance company rejects the demand, then after judgment the insurance company could be on the hook to pay all of the judgment, no matter what the amount.