As long as you were not in any way at fault, insurance companies in Washington cannot raise your rates. I commonly am asked this question by people who are fault-free in automobile crashes. They have insurance; it is required by law that everyone in Washington and Oregon maintain an insurance policy. They have an idea that they should make claims only through the other driver's insurance. Meanwhile, they have medical bills piling up, there car is unfixed, they cannot get in a rental, the other driver's insurance company is requesting that they make a recorded statement, and they don't know what to do.
I typically advise them that, if they have the coverage, they should use their own insurance to alleviate the burden and stress. Most people respond that they would rather not because out of concern that their rates to go up. The fear behind this belief is a myth that every time a collision gets reported to an insurance company, everyone's rates will go up, regardless of fault. To me, this makes no sense.
Virtually everyone would agree that a person should not be punished for being injured through no fault of their own. Fortunately, the Washington State Legislature is an agreement. One of the ways that insurance carriers adjust rates in Washington is by viewing the person's driver's abstract. When the insurance company looks at a driving abstract, it is unlawful for them to consider motor vehicle collisions where the person applying for insurance was not at-fault when adjusting rates. RCW 46.52.130(2)(e)(iii).
Your own insurance carrier has legal duties to look out for your best interests and help you with the claim; the other driver's insurance company does not. For property damage, it is usually faster to go through your insurance company; they will deal directly with the other driver's company to try and recover your deductible. This is required by law. Your own insurer is probably more likely to help with a rental car, too. If you have PIP, your insurance company should pay the reasonable medical expenses, necessarily incurred for collision-related injuries. In short, assuming you were not at-fault for the crash, your rates should not change simply because you reported it to your insurance.