If you spend 1-2 hours a day consistently studying, I would say you would have a chance. I just started self-studying for the AP Psychology Exam as a freshman, which obviously has a lighter course load. AP World has a significant portion of the test for the DBQ and Free Essay Sections, which you would need to practice for by yourself. If you took APUSH or are taking it right now the concepts should be very similar. Keep in mind, however, the amount of work required to take it in 3 months is going to be a lot, and it might interfere with your extracurricular activities.