Do I need to go to a driving school or rally school to get a license?
No, you don't. Getting a license is just paperwork and payment.
Most track racing involves driving schools and rookie licenses. This isn't the case at NASA Rally Sport. The reason why this is different is that on a track, if a novice makes a mistake, it can end up punting someone else off the track. So you don't want inexperienced people put into a situation where they might impact (literally) someone else's race. That situation is different at a rally, however, since each car leaves on it's own minute, if you make a mistake, it will just be you in a ditch. There's no need to separate rookies from experienced drivers, since everyone is separated by time.