When using another person's car, in general the auto insurance on the vehicle by the owner is primary and the insurance carried by the driver is secondary. This means that as long as your boyfriend's insurance carrier finds that you were given permission to drive the car and that it is acceptable by the terms of his policy, then his liability insurance should pay for the other person's damages.

Your insurance would normally be secondary or excess. This would mean if the damages sustained by the other party were over the limits of his liability insurance then your insurance may be gone after next to cover the other party's claim.

Thus your boyfriend should alert his insurance company to the accident you had in his vehicle and the claim that the other party will likely be placing. You should find out if your insurance company will also need to be informed after the cost of the damages are determined.