No you don't, if you have uninsured motorist. Hit your insurance up for the uninsured motorist amount & DV. Your insurance company will go after his insurance company for full restitution afterwards. This is how to make his and your insurance companies fight it out. Also, this is why you pay your insurance company, uninsured motorist if you have it. It doesn't make any difference if it's part or all of the claim. This includes, the full depreciated value amount also.
***There are four separate areas your insurance company can go after the other individuals insurance; Comprehensive & Collision, Property Damage medical or uninsured motorist to pay the entire amount. There doesn't have to be a medical claim against his insurance either. He pays the premium never-the-less. Insurance companies don't want you to know this, as it's generally done in house or thru a lawyer to insurance company alone.***
You need to check with your insurance agent. We have more experience with this, than I care too. If you're not wanting to do this on your own, hire a lawyer to get full compensation.
We learned allot from the lawyers in both accidents, one being a large medical claim. The other individual was clearly the cause of your accident and hopefully this is recorded in your police report. Your insurance can't raise your rates or report an accident on your insurance record. Been there done this already twice already.
The alternative is; to take them to court, either small claims (up to $5,000) or municipal court and sue. Make sure you get a lawyer for either. The individual who hit you or his insurance company is; responsible to make you completely whole by law.
I suggest you talk to your insurance agent separately.