A number of people I know mentioned that it was quite stressful dealing with the insurance companies, both their own insurance company and the other party's insurance company. To reduce further stress, we decided to hire a lawyer. It's OK to have less monetary compensation at the end, we just don't want to go through similar stresses.
Regarding health insurance and auto insurance, the health insurance might cover the medical expense, depending on the insurance company. However, the health insurance company might contact the insurer and either ask the insurer to reimburse the cost from the settlement, or contact the auto insurance company directly.