I had a girlfriend who was involved in a car wreck. She ended up getting two of her vertebrae fused with a platinum plate--she got a $50,000 settlement from the other guy's insurance company. It was a hit-and-run, and the guy did jail time. It was clearly his fault, and it took her almost 18 months to see her money.
As soon as the settlement was complete, HER insurance company demanded something like $30K of the settlement to cover their own losses.
So, if you were to sue, I'd expect your insurance company to do something similar. Unless you were looking at a big-dollar settlement, it probably wouldn't be worth it.