Rear-ended and person at fault is not insured. What should I do?

Several things:

(1) Look at the coverage selections page of YOUR auto insurance or call your agent. If you have underinsured coverage, then your own underinsured coverage should cover your bodiliy injury.

(2) Hopefully you have your own collision coverage to cover your claim for property damages to the car.

(3) You CAN sue the other driver, but first investigate and consider whether s/he has any assets. If not, as a practical matter, what would be the point in suing them in that you can't get blood out of a rock.

(4) Yes, it would likely be best to have an attorney handle this. Most personal injury attorneys give a free initial consultation. This is the sort of troublesome situation I handle all the time in the jurisdictions in which I practice, not WA, by the way, and so legal counsel in WA should be able to guide you through.

You should check your own insurance policy coverage and determine whether you have Uninsured Motorist Coverage (UIM). This would allow you to make a claim for all damages, not just property damages or medical expenses, with your own insurance company. I would recommend that you at least consult with an experienced personal injury lawyer who can review your situation in detail and advise you on how best to proceed and protect your rights. You may find the link below helpful. Good luck.