After a car accident, it is recommended that you immediately seek the services of a car accident law firm. As for statements for the insurance company, you have a duty to cooperate with your insurance company. That duty requires you to give a statement to your insurance company. However, you’re under no duty or obligation to give a statement to the at-fault insurance company.
As for getting in contact with your own insurance, is there a time limit as to when you should contact them? The best thing to do is contact them as soon as possible.