Driving on a flat flexes the internal cord far more than it was designed to take, so the tire casing is compromised to an unknown extent. If you only bop around on surface streets at 40 MPH, you could probably stick with it, but I would not want to run it on a 20-mile freeway commute. A blowout at speed could damage your $$ wheel too. I would make my decision on this and whether a loved one drives that car. Your car may require both tires on the same axle be replaced together, so I understand this can be costly. If so, keep the "good" old tire for the rainy day when this happens again. If you decide to run with it, keep an eye out for any sidewall distortion, bubbles, or pressure loss for the life of the tire.