RE: Would this be wrong and or illegal?
Feral hogs are not covered under the Illinois Game Code so you could go ahead and "hunt" it with your bow.
Ask yourself first, are you doing it to enjoy the experience of the hunt, or are you like so many youngsters, just out going out to kill something. There is a huge difference.
If you go ahead and kill it, better keep your mouth shut or the be kind to animals people will raise cane. It is possible you may also be charged with animal cruelty if the animal is not dispatched in a humane manner.