Auto Insurance: Is it Unwise to Switch Insurance Companies After an Accident

My question involves an injury that occurred in the state of: WV

I was hit by an uninsured driver and she admitted fault. I had a shoulder injury that will require surgery, my mother had a broken collarbone. I have significant uninsured motorist coverage and will be attempting to settle with my own company. My question is my policy expires soon and I have found a much better rate with a different company. Is there any reason not to switch companies or would it be easier/beneficial to continue with my current company until the matter is settled?

Thanks in advance.

Auto Insurance: Is it Unwise to Switch Insurance Companies After an Accident