Your insurance company should cover you, even if you were convicted of a DUI. You need to report the accident as soon as possible. The other party may have already reported it, so you need to contact your carrier to explain all the relevant facts related to the accident.

Typically, the insurance company will pay for the damages and deduct the amount of the deductible from the payment amount. If they pay the check to you, it will be less the deductible. If they pay it to a body shop, the body shop will look to you for the deductible.