If the BBQ sauce was Jack Daniel's brand (mfg by Heinz), they clearly indicate their product does not contain any alcohol. Even if it were Jack Daniel's whiskey added to a home-made concoction, the alcohol should have burned off and you ought to have nothing to worry about.
Although some might criticize me for it on this board, I continue to cook and use recipes that use copious amounts of alcohol. For example, traditional French recipes such as coq au vin and Bœuf bourguignon which call for assertive red wines. The only big difference is that I no longer quaff a bottle or two while cooking.