Hello and welcome to FF! Green frog is a generic name given to many frogs around the world. Need to be more specific or include pics of frogs from above and from side to help ID them.
You could leave a water dish with dechlorinated tap in vehicle to help prevent the frog from dehydrating. A flashlight search at night looking below seats, etc. might help locate it. Injuries can be treated with non-analgesic plain Neosporin. Injured frog should be kept in damp (dechlorinated water) unprinted paper towels changed every couple days until healed. Good luck!