If it were me, I think it would probably be a good idea to start treatment with the insurance you have now, than risk a new insurance plan deciding not to pay at all if they classify your injury as a pre-existing condition. (I honestly have no idea what they would do, but just throwing that out there as a possibility).

This is a good time to educate yourself as to whether you will have the possibility of extending your insurance when/if your job goes away, what that will cost, or whether there is an affordable option to purchase your own health insurance. Get the information you need in order to plan ahead.

www.healthinsurance.com is a good place to look for insurance quotes.