No. Your insurance will hopefully. PIP (personal injury protection) kicks in immediately. Then your insurance goes after them for coverage. At least that's how it works here.
Generally you have to pursue a civil suit for damages relating to injury/ loss of wages or potential wages (outside of PIP coverage).
However, if it's under the state maximum for small claims court, it's a VERY easy process. With medical bills, a doctor's note, and a police record of the accident and the DUI report, you should win easily.
Frankly, if the person can afford it, they should settle out of court to save themselves a potentially bad losing case.