After a car accident, should I go with my insurance provider or the other driver’s?

In Ontario, because of the no fault system you should contact your own insurance company both for the costs of repair of your own car and to claim your accident benefits or no fault benefits

In order to sue for pain and suffering and other losses, you would claim against the insurance company of the at fault driver involved in the motor vehicle accident.

It would be in your best interests to consult a lawyer. You could possibly hurt your insurance claim if you contact the other insurance company on your own.