Can I recuperate money that my personal insurance paid for my healthcare costs if the other driver did not have insurance?

I was involved in a car accident that was the fault of another driver hitting me. That driver did not have car insurance at the moment and therefore my car insurance with a maximum of $25,000 kicked into pay for some of the medical bills but that limit was reached. Therefore my personal health insurance kicked in to pay for those payments medical bills. I was wondering if those expenses did my personal insurance paid could be recuperated for me.